Teaching Taguchi Method to IE
10
Teaching the Taguchi method to industrial engineers Jiju Antony and Frenie Jiju Antony Introduction Dr Genichi Taguchi is a Japanese quality mana gement consulta nt who has develo ped and promoted a philosophy and methodology for continuous quality improv ement in products and processes. Within this philosophy, Taguchi shows how the statistical design of experiments (SDOE or DOE) can help indust rial engineers design and manufacture products that are both of high quality and low cost. His approach is primarily focused on eliminating the causes of poor quality and on making product performance insensitive to variation. DOE is a powerful statistical technique for determining the optimal factor settings of a process and thereby achieving improved process performance, reduced process variability and improved manufacturability of products and processes. Taguchi (1986) advocates the use of orthogonal array designs to assign the factors chosen for the experiment. The most commonly used orthogona l arra y designs are L8 (i.e. eight experimental trials), L16 and L18. The power of the Taguchi method is that it integrates statistical methods into the engineering process. Bendell et al. (1989) and Rowlands et al. (2000) report success of the Taguc hi method in the automotive, pla stics, semiconductors, metal fabrication and foundry industries. However, Antony (1996) suggests that the application of the Taguchi method in the UK manufacturing and service industries is limited and often applied incorrectly. Moreover, a typical remark is ‘‘I can do the text book and class room examples, but I am not comfortable and confident in applying the concepts and principles of DOE in my work area’’. Accordi ng to Antony et al. (Antony et al. 1996a; 1998a; 1998b; 1999; Antony, 1998) the following issues are key to this lack of or improper application of experimental design techniques based on the Taguchi method: The word ‘‘statistics’’ invokes fear in many industrial engineers. Many engineers in the UK leave universities without a complete understanding of the The authors Jiju Antony is at the International Manufacturing Centre, Department of Engineering, University of Warwick, Coventry, UK. Frenie Jiju Antony is at the School of Management Studies, Cochin University of Science and Technology, Kerala , India. Keywords Taguchi methods, Statistical process control, Design of experiments Abstract The Taguchi method (Tm) is a powerful problem solving technique for improving process performance, yield and productivity. It reduces scrap rates, rework costs and manufacturing costs due to excessive variability in processes. However, its application by industrial engineers in the UK is limited, in part due to the inadequate statistical education of engineers. This paper presents a simple experiment which can be used in the classroom to teach engineers the basics of the technique and illustrates simple analytical and graphical tools which promote rapid understanding of the results of the experiment. Electr onic access The research register for this journal is available at http://www.mcbup.com/research_registers The current issue and full text archive of this journal is available at http://www.emerald-library.com/ft
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Transcript of Teaching Taguchi Method to IE
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 19
Teaching the Taguchimethod to industrial
engineers Jiju Antony and
Frenie Jiju Antony
Introduction
Dr Genichi Taguchi is a Japanese quality
management consultant who has developed
and promoted a philosophy and methodology
for continuous quality improvement in
products and processes Within this
philosophy Taguchi shows how the statistical
design of experiments (SDOE or DOE) can
help industrial engineers design and
manufacture products that are both of high
quality and low cost His approach is
primarily focused on eliminating the causes of
poor quality and on making product
performance insensitive to variation DOE is apowerful statistical technique for determining
the optimal factor settings of a process and
thereby achieving improved process
performance reduced process variability and
improved manufacturability of products and
processes
Taguchi (1986) advocates the use of
orthogonal array designs to assign the factors
chosen for the experiment The most
commonly used orthogonal array designs are
L8 (ie eight experimental trials) L16 and
L18 The power of the Taguchi method is
that it integrates statistical methods into the
engineering process Bendell et al (1989) and
Rowlands et al (2000) report success of the
Taguchi method in the automotive plastics
semiconductors metal fabrication and
foundry industries However Antony (1996)
suggests that the application of the Taguchimethod in the UK manufacturing and service
industries is limited and often applied
incorrectly Moreover a typical remark is lsquolsquoI
can do the text book and class room
examples but I am not comfortable and
confident in applying the concepts and
principles of DOE in my work arearsquorsquo
According to Antony et al (Antony et al
1996a 1998a 1998b 1999 Antony 1998)
the following issues are key to this lack of or
improper application of experimental design
techniques based on the Taguchi method
The word lsquolsquostatisticsrsquorsquo invokes fear in
many industrial engineers Many
engineers in the UK leave universities
without a complete understanding of the
power of statistics and are therefore likely
to avoid the use of statistical techniques
in their subsequent careersFew graduating engineers have been
exposed to applied statistical quality
techniques such as DOE robust design
The authors
Jiju Antony is at the International Manufacturing Centre
Department of Engineering University of Warwick
Coventry UK
Frenie Jiju Antony is at the School of Management
Studies Cochin University of Science and Technology
Kerala India
Keywords
Taguchi methods Statistical process control
Design of experiments
Abstract
The Taguchi method (Tm) is a powerful problem solving
technique for improving process performance yield and
productivity It reduces scrap rates rework costs and
manufacturing costs due to excessive variability in
processes However its application by industrial engineers
in the UK is limited in part due to the inadequate
statistical education of engineers This paper presents a
simple experiment which can be used in the classroom to
teach engineers the basics of the technique and illustrates
simple analytical and graphical tools which promote rapid
understanding of the results of the experiment
Electronic access
The research register for this journal is available at
httpwwwmcbupcomresearch_registers
The current issue and full text archive of this journal is
available at
httpwwwemerald-librarycomft
141
Work Study
Volume 50 Number 4 2001 pp 141plusmn149
MCB University Press ISSN 0043-8022
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 29
etc This is another symptom of the
statistical education of the engineering
fraternity
Engineers consistently avoid the use of
applied statistical techniques in tackling
process optimisation and quality control
problems Where techniques are in use
eg the use of control charts for process
analysis and monitoring there often
appears to be a lack of a full
understanding of the basic and
fundamental principles behind their
application (Morrison 1997)
Many textbooks and courses on DOE
primarily focus on the statistical analysis of the problem under study However this is
but one component of DOE which involves
planning design execution analysis and
interpretation of results
A lack of communication between the
academic and industrial worlds and
between functional specialists restricts the
application of the Taguchi method
(Tm)and DOE (Antony et al 1998a) Itis important though too rare that
quality manufacturing process design
and operational departments
communicate and work effectively with
one another
Potential applications and benefits ofusing the Taguchi method
The Taguchi method has wide application in
manufacturing organisations Table I
illustrates the application of Tm in the
plastics automotive process metal
fabrication food and electronics and semi-
conductor sectors (Rowlands et al 2000)
Typical applications in service industry
The use of Tm in service industries is not
often reported This may be because
service performance is often more
difficult to measure
the performance of a service process
depends a great deal on the behaviour
and attitude of the service provider and it
varies with time andthe identification and measurement of
control factors and their influence on
performance characteristic(s) is often
difficult
However there clearly are possible applications
of Tm in the service sector Examples include
reducing the time taken to respond to
customer complaints
reducing errors on service orders and
reducing the length of stay in an
emergency room in hospital
If the use of Tm is to become more prevalent
ways must be found to teach engineers (and
others) effectively how to apply it successfully
Steps in performing a Taguchiexperiment
The process of performing a Taguchi
experiment follows a number of distinct steps
Table I Typical applications of Tm in manufacturing
Processproduct Nature of problem Experiment size Benefits
Injection moulding
process
High scrap rate due to
excessive process variability
8 trials Annual savings were
estimated to be over
pound40000
Diesel injector High rework rate 16 trials Annual savings were
estimated to be over
pound10000
Welding process Low weld strength 16 trials Annual savings were
estimated to be over
pound16000
Chemical process Low process yield 8 trials Process yield was improved
by over 10 per cent
BiscuitExcessive variability inbiscuit length
16 trials Biscuit length variability wasreduced by over 25 per cent
Wire-bonding process Low wire pull strength 16 trials Annual savings were over
pound30000
142
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 39
Step1 formulation of the problem ndash the
success of any experiment is dependent
on a full understanding of the nature of
the problem
Step 2 identification of the output
performance characteristics m ost relevant
to the problemStep 3 identification of control factors
noise factors and signal factors (if any)
Control factors are those which can be
controlled under normal production
conditions Noise factors are those which
are either too difficult or too expensive to
control under normal production
conditions Signal factors are those which
affect the mean performance of the
process
Step 4 selection of factor levels possibleinteractions and the degrees of freedom
associated with each factor and the
interaction effects
Step 5 design of an appropriate
orthogonal array (OA)
Step 6 preparation of the experiment
Step 7 running of the experiment with
appropriate data collection
Step 8 statistical analysis and
interpretation of experimental results
Step 9 undertaking a confirmatory run of the experiment
Paper helicopter experiment
In many academic institutions within the UK
the focus of engineering statistics is on the
theory of probability (for example card
shuffling dice rolling etc) the mathematical
aspects of probability and probability
distributions (eg normal exponentialbinomial Poisson log-normal etc)
hypothesis tests etc Quality improvement
techniques (DOE Tm SPC etc) are often
not covered Understandably graduates are
not confident about using such techniques at
their place of work
As part of an exercise to increase the
awareness of Tm amongst industrial
engineers the authors used a simple paper
helicopter experiment readily used in
academic institutions Due to a limitedamount of time one member from each
group in the class was involved with the
experimental work However the students
were all asked to analyse and interpret the
data (on an individual basis) The results of
the analysis were discussed in the classroom
as part of the process of gaining an
understanding of experimental objectives and
process
The paper helicopter experiment is quite
well known among engineers and statisticians
in both the academic and industrial worldsMany industrial training programmes on Tm
use it in some form However they often focus
on the design and analysis of the experiment
without providing guidance to engineers on
the interpretation of results from the analysis
Moreover many courses do not cover the
importance of careful experimental planning
for the success of any industrially designed
experiment
The purpose of this experiment was to
provide undergraduate engineering studentswith an understanding of the role of
Taguchirsquos lsquolsquoparameter designrsquorsquo (sometimes
called lsquolsquorobust designrsquorsquo) in tackling both
product and process quality-related problems
in real-life situations Parameter design is a
well established methodology for improving
product and process quality at minimal cost
by reducing the effect of undesirable external
influences which cause variation in product or
process performance (Phadke 1989)
The objective of the exercise was to identifythe optimal settings of control factors which
would maximise the flight time of paper
helicopters (with minimum variation) Here
control factors refer to those which can be
easily controlled and varied by the designer or
operator in normal production conditions A
brainstorming session by a group of students
identified six control factors which were
thought to influence the time of flight (refer to
Table II) Brainstorming should be
considered an integral part of the Taguchimethodology ndash it is a useful technique in
identifying the most influential factors in an
experiment
In order to simplify the experiment each
factor was studied at two levels The lsquolsquolevelrsquorsquo
of a factor here refers to the specified value of
Table II Control factors and their range of settings for the experiment
Control factor Labels Level 1 Level 2
Paper type A Regular Bond
Body length B 8cm 12cm
Wing length C 8cm 12cm
Body width D 2cm 3cm
Number of clips E 1 2
Wing shape F Flat Angled
143
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 49
a setting For example in the experiment
body width was studied at 2cm and 3cm
Factors at three (and higher) levels make
analysis more complicated ndash and are therefore
not used in awareness-raising sessions
Having identified the control factors it is
important to list the interactions which are to
be studied for the experiment Interaction
exists when the effect of one factor is not the
same at different levels of the other factor An
effect refers to the change in response due to
the change in level of a factor (Antony et al
1998b) Consider for example the factors
wing length and body length of the paper
helicopter Assume each factor was kept attwo-levels for the study Time of flight is the
response (or quality characteristic) of interest
Interaction between wing length and body
length exists when the effect of wing length on
time of flight at two different levels of body
length is different
For this experiment three interactions were
identified (from the brainstorming session) as
being of interest(1) body length pound wing length (B pound C or
BC)
(2) body length pound body width (B pound D or
BD) and
(3) paper type pound body length (A pound B or AB)
The following noise factors were identified (as
having some impact on the flight time but
being difficult to control)
operator-to-operator variationdraughts
reaction time and
ground surface
One aim was to determine the control factor
settings which would best dampen the effect
of these noise factors According to Taguchi
there is an optimal combination of factor
settings which counters the effects of noise In
order to minimise the effect of these noise
factors the same student was responsible for
all timings ndash reducing the effects of variable
reaction times when hitting the stopwatch
upon release of the helicopter and its hitting
the ground
Figure 1 illustrates a template for the model
of a paper helicopter which can be made from
an A4 size paper It forms the basis of a simple
experiment requiring only simple items such
as paper scissors and paper clips It takesabout six hours to design the experiment
collect the data and then perform the
statistical analysis (with the lsquolsquoexperimentrsquorsquo
itself taking about 90 minutes) In this case
the statistical analysis was executed as a
homework assignment though the results
were discussed in the classroom in detail
Choice of orthogonal array design
The choice of a suitable orthogonal array
(OA) design is critical for the success of an
experiment and depends on the total degrees
of freedom required to study the main and
interaction effects the goal of the experiment
resources and budget available and time
constraints Orthogonal arrays allow one to
compute the main and interaction effects via a
minimum number of experimental trials(Ross 1988) lsquolsquoDegrees of freedomrsquorsquo refers to
the number of fair and independent
comparisons that can be made from a set of
observations In the context of SDOE the
number of degrees of freedom is one less than
the number of levels associated with the
factor In other words the number of degrees
of freedom associated with a factor at p-levels
is ( p-1) As the number of degrees of freedom
associated with a factor at two levels is unity
in the present example the number of degrees
of freedom for studying the six main effects is
equal to six The number of degrees of
freedom associated with an interaction is the
product of the number of degrees of freedom
associated with each main effect involved in
the interaction (Antony 1998) In this simple
case the number of degrees of freedom for
studying the three interaction effects is equalto three Therefore the total degrees of
freedom is equal to nine (ie 6 + 3) It is
important to notice that the number of
Figure 1 Template for paper helicopter design
144
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 59
experimental trials must be greater than the
total degrees of freedom required for studying
the effects The standard OAs for factors with
two levels are L 4 L 8 L 1 6 L 32 and so on Here
the notation lsquolsquoLrsquorsquo implies that the information
is based on the Latin square arrangement of
factors A Latin square arrangement is a
square matrix arrangement of factors with
separable factor effects Here the numbers 4
8 12 16 etc denote the number of
experimental trials For the helicopter
experiment as the total degrees of freedom is
equal to nine the closest number of
experimental trials that can be employed for
the experiment is 16 (ie L 1 6 OA) Having
identified the most suitable OA the next step
was to assign the main and interaction effects
to various columns of the array A standard
L 16 OA (see Appendix) contains 15 columns
for either studying 15 main effects or a
combination of main and interaction effects
so that the degrees of freedom will add up to
15 In the present example there are only six
main and three interaction effects Thismeans that only nine columns out of 15 are
used For example factor D (refer to Table
III) was assigned to column 1 and factor C to
column 2 Column 3 is empty (see Table III)
as the interaction between these factors was of
no interest in this experiment Using the
standard linear graphs and OA (Ross 1988)
the remaining factors and interactions were
assigned to the columns of an L 1 6 in the
following manner
Column 1 ndash body width (D) column 2 ndash
wing length (C) column 4 ndash body length (B)
column 5 ndash body width pound body length (B poundD) column 6 ndash wing length pound body length (B
poundC) column 7 ndash wing shape (F) column 8 ndash
paper type (A) column 12 ndash body length poundpaper type (AB) and column 14 ndash number of
clips (E)
The experimental layout showing all the
factors and interactions along with the flight
times (measured in seconds) is shown in
Table III As each factor was studied at two
levels coded level 1 represents the low level of
a factor setting and level 2 represents the high
level setting Each experiment was replicated
in order to capture variation in results due to
uncontrolled noise
Statistical analysis and interpretation ofresults
In Taguchirsquos parameter design the basic
objective is to identify the conditions whichoptimise processproduct performance In
arriving at this optimal set of conditions
Taguchi advocates the use of signal-to-noise
ratio (SNR) ndash the need is to maximise the
performance of a system or product by
minimising the effect of noise while
maximising the mean performance The SNR
is treated as a response (output) of the
experiment which is a measure of variation
when uncontrolled noise factors are present in
Table III Experimental layout
Column no 1 2 4 5 6 7 8 12 14
Factorsinteractions D C B BD BC F A AB E Flight time
Trial no
1 1 1 1 1 1 1 1 1 1 276 283
2 1 1 1 1 1 1 2 2 2 220 213
3 1 1 2 2 2 2 1 2 2 193 230
4 1 1 2 2 2 2 2 1 1 219 210
5 1 2 1 1 2 2 1 1 2 240 250
6 1 2 1 1 2 2 2 2 1 282 231
7 1 2 2 2 1 1 1 2 1 339 301
8 1 2 2 2 1 1 2 1 2 262 239
9 2 1 1 2 1 2 1 1 1 246 212
10 2 1 1 2 1 2 2 2 2 208 190
11 2 1 2 1 2 1 1 2 2 214 229
12 2 1 2 1 2 1 2 1 1 205 212
13 2 2 1 2 2 1 1 1 2 296 27014 2 2 1 2 2 1 2 2 1 247 260
15 2 2 2 1 1 2 1 2 1 262 291
16 2 2 2 1 1 2 2 1 2 232 241
145
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 69
the system (Antony et al 1999) Taguchi has
developed and defined over 60 different
SNRs for engineering applications of
parameter design For the present study as
the objective was to maximise time of flight it
was decided to select the SNR related to
larger-the-better (LTB) qualitycharacteristics This is generally used for
quality characteristics such as strength fuel
efficiency process yield life of a component
and so on For LTB quality characteristics
the SNR is given by the following equation
SNR ˆ iexcl10logpound 1
ncurren
1
y2i
currenhellip1dagger
where n = number of values at each trial
condition (ie 2 from Table II) and yi = each
observed valueTable IV illustrates the SNR values (based
on equation 1) corresponding to each trial
condition
Table V illustrates the average SNR values
(SNR) at low (level 1) and high (level 2) levels
and the effect of each main and interaction
effect on the SNR
Sample calculation for factor lsquolsquoCrsquorsquo
Average SNR at level 1 of factor lsquolsquoCrsquorsquo =
SNRC 2 = 18 [893 + 671 + 641 + 662
+712 + 595 + 689 + 638]
= 688
Similarly average SNR at level 2 of factor
lsquolsquoCrsquorsquo = SNRC 2 = 18 [778 + 805 + 1006 +
795 + 901 + 807 + 880 + 747]
= 840
Effect = SNRC 2 - SNRC 1
= 840 - 688 = 152
The other main and interaction effects were
calculated in a similar manner (see Table V)
Having obtained the average SNR values
the next step is the identification of significant
main and interaction effects which influence
the SNR To achieve this a powerful
graphical tool called half-normal probabilityplots (HNPP) is useful
A half-normal probability plot (HNPP) is
obtained by plotting the absolute values of the
effects (both main andor interaction effects)
along the X-axis and the per cent probability
along the Y-axis The per cent probability
can be obtained by using the following
equation
P i ˆhellipi iexcl 0
5dagger
npound 100 hellip2dagger
where n = number of estimated effects
(n = 15) and i is the rank of the estimated
effect when arranged in the ascending order of
magnitude (eg for factor C i = 15)
Figure 2 illustrates the HNPP of the factor
and interaction effects for the helicopter
experiment The computer software package
lsquolsquoDesign-easersquorsquo was used to construct the plot
Those effects which are active and real will
fall off the straight line whereas the inactive
and insignificant effects will fall along the
straight line (Daniel 1959) The figure
reveals that main effects A C E and F are
statistically significant ie paper type wing
length number of clips and wing shape are
statistically significant In order to support
and justify this claim another graphical tool
(main effects plot) is used This shows the
average SNR values at low and high level
settings of each factor Figure 3 illustrates the
main effects plot for the paper helicopter
experiment (using the values from Table V)
This graphical aid provides non-statisticians
with a better picture of the importance of the
effects of the chosen control factors The
slope of the line is an indication of the
importance of a main or interaction effect
The figure shows that the most dominant
factor is the wing length followed by paper
type wing shape and number of clips As each
factor was chosen at two levels the effect of
Table IV SNR table
Trial number SNR Trial number SNR1 893 9 712
2 671 10 595
3 641 11 689
4 662 12 638
5 778 13 901
6 805 14 807
7 1006 15 880
8 795 16 747
Table V Average SNR table
Factors or interactions D C B BD BC F A AB E
SNR 1 781 688 770 763 787 800 812 766 800
SNR 2 746 840 757 765 740 727 715 762 728
Effect estimate plusmn035 152 plusmn013 002 plusmn047 plusmn073 plusmn097 plusmn004 plusmn072
146
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 79
each factor must be assumed to be linear If non-linear effects are to be studied it is
necessary to choose more than two levels for
each factor However it is good practice to
start off an experiment with two levels and
then perform smaller sequential experiments
at higher levels to gain a better understanding
of the nature of the process
For this experiment none of the interaction
effects is significant Consider for example
the interaction between the body length and
body width In order to compute thisinteraction the first step is to compute the
average SNR values at each of the four
combinations of the factor levels Table VI
shows the average SNR values for these four
combinations
An interaction plot is useful in providing a
rapid understanding of the nature of
interactions (Schmidt and Launsby 1992)
Interaction plots are constructed by plotting
the average response values (in this case SNR
values) at each factor level combination
Parallel lines are an indication of the absenceof interaction between the factors whereas
non-parallel lines are an indication of the
presence of interaction between the factors
Figure 4 shows that the effect of body width
on the flight time at both levels of body length
is the same In other words the effect of body
width on the flight time is the same
irrespective of the level of body length This
implies the absence of interaction between
these two factors
Determination of the optimal controlfactor settings
The selection of optimal settings depends on
the objective of the experiment or the nature
of the problem under study For the
helicopter example the objective was to
maximise the flight time In Taguchi
experiments the objective is to identify the
factor settings which yield the highest SNR ndash
these settings will generally produce a
consistent and reliable product Moreover
the process which produces the product will
Figure 2 Half-normal plot of effects
Figure 3 Main effects plot of the control factors
Table VI Average SNR values
Body le ngth Body widt h Aver age SNR
1 1 787
1 2 754
2 1 776
2 2 739
Figure 4 Interaction plot between body length and body width
147
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 89
be insensitive to various sources of
uncontrollable variation For the paper
helicopter experiment the optimal control
factor settings based on the highest SNR have
been determined These are shown in Table
VII In order to decide which level is better for
maximising flight time the SNR values at
both low (level 1) and high (level 2) levels of
each factor are compared
Once the optimal settings are established it
is useful to undertake a confirmation trial
before onward actions are undertaken
(Antony 1996) Three helicopters were made
using the optimal factor settings and the
average flight time was recorded as 356
seconds This shows an improvement of
above 30 per cent on the average flight time
using the range of variable settings The
results also reveal that flight time increases for
larger wing length and smaller body length
Summary and conclusions
The experiment was carried out with the aim
of optimising the flight time of a paper
helicopter In order to study the effect of
variables and the possible interactions
between them in a minimum number of trials
the Taguchi approach to experimental design
was adopted As the experiment itself was
simple the students found it to be a clear
illustration of the process of
defining the problem
identifying the control variables and
possible interactions
defining the required levels for each
variablefactor
determining the response of interest
selecting the most suitable orthogonal
array
performing the experiment
undertaking the analysis andinterpreting the results to obtain a better
understanding of the situation under
review
The Taguchi method is a powerful
approach to address process variability and
optimisation problems However the
application of SDOE and Tm by the
engineering fraternity in UK organisations
is limited due in part to a shortage of skills
in problem solving and inadequate
statistical knowledge This paper
demonstrates a simple means of introducing
students to this powerful tool The
approach uses a simple paper helicopter
experiment For simplicity all control
parameters were studied at two levels This
mirrors actual practice ndash in most
optimisation problems factors at two levelsare the most widely used (Gunst and
Mason 1991 Lucas 1992) The paper
helicopter experiment is quite old and has
been widely used by many statisticians for
teaching purposes However this approach
has focused on minimal statistical jargon
and number crunching and on the use of
modern graphical tools to achieve a rapid
understanding of the results from the
statistical analysis The authors strongly
believe that the experiment provides a
simple and beneficial way to help engineers
approach experimental design in a way that
ensures it is transferrable to their own work
environment
References
Antony J (1996) ``A strategic methodology to the use of
advanced statistical quality control techniquesrsquorsquo
PhD thesisAntony J (1998) ``Some key things industrial engineers
should know about experimental designrsquorsquo Logistics
Information Management 1998 Vol 11 No 6
pp 386-92
Antony J et al (1996) ``Optimisation of core tube life
using Taguchi experimental design methodologyrsquorsquo
Journal of Quality World (Technical Supplement)
IQA March pp 42-50Antony J et al (1998a) ``A strategic methodology to the
use of advanced statistical quality improvement
techniquesrsquorsquo The TQM Magazine (The International
Bi-Monthly for TQM) Vol 10 No 3 pp 169-176
Antony J et al (1998b) ``Key interactionsrsquorsquo Journal of Manufacturing Engineer IEE Vol 77 No 3
pp 136-8
Antony J et al (1999) Experimental Quality plusmn A Strategic
Approach to Achieve and Improve Quality Kluwer
Academic Publishers Dordrecht December
Bendell A (Ed) (1989) Taguchi Methods Applications in World Industry IFS Publications Bedford
Daniel C (1959) ``Use of half-normal plots in interpreting
factorial two level experimentsrsquorsquo Technometrics
Vol 1 No 4 pp 53-70
Table VII Optimal control factor settings
Control factors Optimum level
Paper type Regular (level 1)
Body length 8cm (level 1)
Wing length 12cm (level 2)Body width 2cm (level 1)
Number of clips 1 (level 1)
Wing shape Flat (level 1)
148
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 99
Gunst RF and Mason RL (1991) How to Construct Fractional Factorial Experiments ASQC Statistics
Division ASQC Press Milwaukee MI
Lucas JM (1992) ``Split plotting and randomisation inindustrial experimentsrsquorsquo ASQC Quality Congress
Transactions Nashville TN pp 374-82Morrison JM (1997) ``Statistical engineering plusmn the keyto qualityrsquorsquo Engineering Science and Education
Journal pp 123-7Phadke MS (1989) Quality Engineering using Robust
Design Prentice-Hall International Englewood
Cliffs NJ
Ross PJ (1988) Taguchi Techniques for Quality Engineering McGraw-Hill Publishers New York NY
Rowlands H Antony J and Knowles G (2000) ``An
application of experimental design for processoptimisationrsquorsquo The TQM Magazine Vol 12 No2
pp 78-83Schmidt SR and Launsby RG (1992) Understanding Industrial Designed Experiments Air Academy
Press Washington DCTaguchi G (1986) Introduction to Quality
Engineering Asian Productivity Organisation
Tokyo
Appendix
Table AI Coded design matrix of an L16 (21 5
) orthogonal array
Column
Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2
3 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2
4 1 1 1 2 2 2 2 2 2 2 2 1 1 1 1
5 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2
6 1 2 2 1 1 2 2 2 2 1 1 2 2 1 1
7 1 2 2 2 2 1 1 1 1 2 2 2 2 1 1
8 1 2 2 2 2 1 1 2 2 1 1 1 1 2 2
9 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
10 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1
11 2 1 2 2 1 2 1 1 2 1 2 2 1 2 1
12 2 1 2 2 1 2 1 2 1 2 1 1 2 1 2
13 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1
14 2 2 1 1 2 2 1 2 1 1 2 2 1 2 1
15 2 2 1 2 1 1 2 1 2 2 1 2 1 1 2
16 2 2 1 2 1 1 2 2 1 1 2 1 2 2 1
149
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
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etc This is another symptom of the
statistical education of the engineering
fraternity
Engineers consistently avoid the use of
applied statistical techniques in tackling
process optimisation and quality control
problems Where techniques are in use
eg the use of control charts for process
analysis and monitoring there often
appears to be a lack of a full
understanding of the basic and
fundamental principles behind their
application (Morrison 1997)
Many textbooks and courses on DOE
primarily focus on the statistical analysis of the problem under study However this is
but one component of DOE which involves
planning design execution analysis and
interpretation of results
A lack of communication between the
academic and industrial worlds and
between functional specialists restricts the
application of the Taguchi method
(Tm)and DOE (Antony et al 1998a) Itis important though too rare that
quality manufacturing process design
and operational departments
communicate and work effectively with
one another
Potential applications and benefits ofusing the Taguchi method
The Taguchi method has wide application in
manufacturing organisations Table I
illustrates the application of Tm in the
plastics automotive process metal
fabrication food and electronics and semi-
conductor sectors (Rowlands et al 2000)
Typical applications in service industry
The use of Tm in service industries is not
often reported This may be because
service performance is often more
difficult to measure
the performance of a service process
depends a great deal on the behaviour
and attitude of the service provider and it
varies with time andthe identification and measurement of
control factors and their influence on
performance characteristic(s) is often
difficult
However there clearly are possible applications
of Tm in the service sector Examples include
reducing the time taken to respond to
customer complaints
reducing errors on service orders and
reducing the length of stay in an
emergency room in hospital
If the use of Tm is to become more prevalent
ways must be found to teach engineers (and
others) effectively how to apply it successfully
Steps in performing a Taguchiexperiment
The process of performing a Taguchi
experiment follows a number of distinct steps
Table I Typical applications of Tm in manufacturing
Processproduct Nature of problem Experiment size Benefits
Injection moulding
process
High scrap rate due to
excessive process variability
8 trials Annual savings were
estimated to be over
pound40000
Diesel injector High rework rate 16 trials Annual savings were
estimated to be over
pound10000
Welding process Low weld strength 16 trials Annual savings were
estimated to be over
pound16000
Chemical process Low process yield 8 trials Process yield was improved
by over 10 per cent
BiscuitExcessive variability inbiscuit length
16 trials Biscuit length variability wasreduced by over 25 per cent
Wire-bonding process Low wire pull strength 16 trials Annual savings were over
pound30000
142
Teaching the Taguchi method to industrial engineers
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832019 Teaching Taguchi Method to IE
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Step1 formulation of the problem ndash the
success of any experiment is dependent
on a full understanding of the nature of
the problem
Step 2 identification of the output
performance characteristics m ost relevant
to the problemStep 3 identification of control factors
noise factors and signal factors (if any)
Control factors are those which can be
controlled under normal production
conditions Noise factors are those which
are either too difficult or too expensive to
control under normal production
conditions Signal factors are those which
affect the mean performance of the
process
Step 4 selection of factor levels possibleinteractions and the degrees of freedom
associated with each factor and the
interaction effects
Step 5 design of an appropriate
orthogonal array (OA)
Step 6 preparation of the experiment
Step 7 running of the experiment with
appropriate data collection
Step 8 statistical analysis and
interpretation of experimental results
Step 9 undertaking a confirmatory run of the experiment
Paper helicopter experiment
In many academic institutions within the UK
the focus of engineering statistics is on the
theory of probability (for example card
shuffling dice rolling etc) the mathematical
aspects of probability and probability
distributions (eg normal exponentialbinomial Poisson log-normal etc)
hypothesis tests etc Quality improvement
techniques (DOE Tm SPC etc) are often
not covered Understandably graduates are
not confident about using such techniques at
their place of work
As part of an exercise to increase the
awareness of Tm amongst industrial
engineers the authors used a simple paper
helicopter experiment readily used in
academic institutions Due to a limitedamount of time one member from each
group in the class was involved with the
experimental work However the students
were all asked to analyse and interpret the
data (on an individual basis) The results of
the analysis were discussed in the classroom
as part of the process of gaining an
understanding of experimental objectives and
process
The paper helicopter experiment is quite
well known among engineers and statisticians
in both the academic and industrial worldsMany industrial training programmes on Tm
use it in some form However they often focus
on the design and analysis of the experiment
without providing guidance to engineers on
the interpretation of results from the analysis
Moreover many courses do not cover the
importance of careful experimental planning
for the success of any industrially designed
experiment
The purpose of this experiment was to
provide undergraduate engineering studentswith an understanding of the role of
Taguchirsquos lsquolsquoparameter designrsquorsquo (sometimes
called lsquolsquorobust designrsquorsquo) in tackling both
product and process quality-related problems
in real-life situations Parameter design is a
well established methodology for improving
product and process quality at minimal cost
by reducing the effect of undesirable external
influences which cause variation in product or
process performance (Phadke 1989)
The objective of the exercise was to identifythe optimal settings of control factors which
would maximise the flight time of paper
helicopters (with minimum variation) Here
control factors refer to those which can be
easily controlled and varied by the designer or
operator in normal production conditions A
brainstorming session by a group of students
identified six control factors which were
thought to influence the time of flight (refer to
Table II) Brainstorming should be
considered an integral part of the Taguchimethodology ndash it is a useful technique in
identifying the most influential factors in an
experiment
In order to simplify the experiment each
factor was studied at two levels The lsquolsquolevelrsquorsquo
of a factor here refers to the specified value of
Table II Control factors and their range of settings for the experiment
Control factor Labels Level 1 Level 2
Paper type A Regular Bond
Body length B 8cm 12cm
Wing length C 8cm 12cm
Body width D 2cm 3cm
Number of clips E 1 2
Wing shape F Flat Angled
143
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Jiju Antony and Frenie Jiju Antony
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832019 Teaching Taguchi Method to IE
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a setting For example in the experiment
body width was studied at 2cm and 3cm
Factors at three (and higher) levels make
analysis more complicated ndash and are therefore
not used in awareness-raising sessions
Having identified the control factors it is
important to list the interactions which are to
be studied for the experiment Interaction
exists when the effect of one factor is not the
same at different levels of the other factor An
effect refers to the change in response due to
the change in level of a factor (Antony et al
1998b) Consider for example the factors
wing length and body length of the paper
helicopter Assume each factor was kept attwo-levels for the study Time of flight is the
response (or quality characteristic) of interest
Interaction between wing length and body
length exists when the effect of wing length on
time of flight at two different levels of body
length is different
For this experiment three interactions were
identified (from the brainstorming session) as
being of interest(1) body length pound wing length (B pound C or
BC)
(2) body length pound body width (B pound D or
BD) and
(3) paper type pound body length (A pound B or AB)
The following noise factors were identified (as
having some impact on the flight time but
being difficult to control)
operator-to-operator variationdraughts
reaction time and
ground surface
One aim was to determine the control factor
settings which would best dampen the effect
of these noise factors According to Taguchi
there is an optimal combination of factor
settings which counters the effects of noise In
order to minimise the effect of these noise
factors the same student was responsible for
all timings ndash reducing the effects of variable
reaction times when hitting the stopwatch
upon release of the helicopter and its hitting
the ground
Figure 1 illustrates a template for the model
of a paper helicopter which can be made from
an A4 size paper It forms the basis of a simple
experiment requiring only simple items such
as paper scissors and paper clips It takesabout six hours to design the experiment
collect the data and then perform the
statistical analysis (with the lsquolsquoexperimentrsquorsquo
itself taking about 90 minutes) In this case
the statistical analysis was executed as a
homework assignment though the results
were discussed in the classroom in detail
Choice of orthogonal array design
The choice of a suitable orthogonal array
(OA) design is critical for the success of an
experiment and depends on the total degrees
of freedom required to study the main and
interaction effects the goal of the experiment
resources and budget available and time
constraints Orthogonal arrays allow one to
compute the main and interaction effects via a
minimum number of experimental trials(Ross 1988) lsquolsquoDegrees of freedomrsquorsquo refers to
the number of fair and independent
comparisons that can be made from a set of
observations In the context of SDOE the
number of degrees of freedom is one less than
the number of levels associated with the
factor In other words the number of degrees
of freedom associated with a factor at p-levels
is ( p-1) As the number of degrees of freedom
associated with a factor at two levels is unity
in the present example the number of degrees
of freedom for studying the six main effects is
equal to six The number of degrees of
freedom associated with an interaction is the
product of the number of degrees of freedom
associated with each main effect involved in
the interaction (Antony 1998) In this simple
case the number of degrees of freedom for
studying the three interaction effects is equalto three Therefore the total degrees of
freedom is equal to nine (ie 6 + 3) It is
important to notice that the number of
Figure 1 Template for paper helicopter design
144
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experimental trials must be greater than the
total degrees of freedom required for studying
the effects The standard OAs for factors with
two levels are L 4 L 8 L 1 6 L 32 and so on Here
the notation lsquolsquoLrsquorsquo implies that the information
is based on the Latin square arrangement of
factors A Latin square arrangement is a
square matrix arrangement of factors with
separable factor effects Here the numbers 4
8 12 16 etc denote the number of
experimental trials For the helicopter
experiment as the total degrees of freedom is
equal to nine the closest number of
experimental trials that can be employed for
the experiment is 16 (ie L 1 6 OA) Having
identified the most suitable OA the next step
was to assign the main and interaction effects
to various columns of the array A standard
L 16 OA (see Appendix) contains 15 columns
for either studying 15 main effects or a
combination of main and interaction effects
so that the degrees of freedom will add up to
15 In the present example there are only six
main and three interaction effects Thismeans that only nine columns out of 15 are
used For example factor D (refer to Table
III) was assigned to column 1 and factor C to
column 2 Column 3 is empty (see Table III)
as the interaction between these factors was of
no interest in this experiment Using the
standard linear graphs and OA (Ross 1988)
the remaining factors and interactions were
assigned to the columns of an L 1 6 in the
following manner
Column 1 ndash body width (D) column 2 ndash
wing length (C) column 4 ndash body length (B)
column 5 ndash body width pound body length (B poundD) column 6 ndash wing length pound body length (B
poundC) column 7 ndash wing shape (F) column 8 ndash
paper type (A) column 12 ndash body length poundpaper type (AB) and column 14 ndash number of
clips (E)
The experimental layout showing all the
factors and interactions along with the flight
times (measured in seconds) is shown in
Table III As each factor was studied at two
levels coded level 1 represents the low level of
a factor setting and level 2 represents the high
level setting Each experiment was replicated
in order to capture variation in results due to
uncontrolled noise
Statistical analysis and interpretation ofresults
In Taguchirsquos parameter design the basic
objective is to identify the conditions whichoptimise processproduct performance In
arriving at this optimal set of conditions
Taguchi advocates the use of signal-to-noise
ratio (SNR) ndash the need is to maximise the
performance of a system or product by
minimising the effect of noise while
maximising the mean performance The SNR
is treated as a response (output) of the
experiment which is a measure of variation
when uncontrolled noise factors are present in
Table III Experimental layout
Column no 1 2 4 5 6 7 8 12 14
Factorsinteractions D C B BD BC F A AB E Flight time
Trial no
1 1 1 1 1 1 1 1 1 1 276 283
2 1 1 1 1 1 1 2 2 2 220 213
3 1 1 2 2 2 2 1 2 2 193 230
4 1 1 2 2 2 2 2 1 1 219 210
5 1 2 1 1 2 2 1 1 2 240 250
6 1 2 1 1 2 2 2 2 1 282 231
7 1 2 2 2 1 1 1 2 1 339 301
8 1 2 2 2 1 1 2 1 2 262 239
9 2 1 1 2 1 2 1 1 1 246 212
10 2 1 1 2 1 2 2 2 2 208 190
11 2 1 2 1 2 1 1 2 2 214 229
12 2 1 2 1 2 1 2 1 1 205 212
13 2 2 1 2 2 1 1 1 2 296 27014 2 2 1 2 2 1 2 2 1 247 260
15 2 2 2 1 1 2 1 2 1 262 291
16 2 2 2 1 1 2 2 1 2 232 241
145
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
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832019 Teaching Taguchi Method to IE
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the system (Antony et al 1999) Taguchi has
developed and defined over 60 different
SNRs for engineering applications of
parameter design For the present study as
the objective was to maximise time of flight it
was decided to select the SNR related to
larger-the-better (LTB) qualitycharacteristics This is generally used for
quality characteristics such as strength fuel
efficiency process yield life of a component
and so on For LTB quality characteristics
the SNR is given by the following equation
SNR ˆ iexcl10logpound 1
ncurren
1
y2i
currenhellip1dagger
where n = number of values at each trial
condition (ie 2 from Table II) and yi = each
observed valueTable IV illustrates the SNR values (based
on equation 1) corresponding to each trial
condition
Table V illustrates the average SNR values
(SNR) at low (level 1) and high (level 2) levels
and the effect of each main and interaction
effect on the SNR
Sample calculation for factor lsquolsquoCrsquorsquo
Average SNR at level 1 of factor lsquolsquoCrsquorsquo =
SNRC 2 = 18 [893 + 671 + 641 + 662
+712 + 595 + 689 + 638]
= 688
Similarly average SNR at level 2 of factor
lsquolsquoCrsquorsquo = SNRC 2 = 18 [778 + 805 + 1006 +
795 + 901 + 807 + 880 + 747]
= 840
Effect = SNRC 2 - SNRC 1
= 840 - 688 = 152
The other main and interaction effects were
calculated in a similar manner (see Table V)
Having obtained the average SNR values
the next step is the identification of significant
main and interaction effects which influence
the SNR To achieve this a powerful
graphical tool called half-normal probabilityplots (HNPP) is useful
A half-normal probability plot (HNPP) is
obtained by plotting the absolute values of the
effects (both main andor interaction effects)
along the X-axis and the per cent probability
along the Y-axis The per cent probability
can be obtained by using the following
equation
P i ˆhellipi iexcl 0
5dagger
npound 100 hellip2dagger
where n = number of estimated effects
(n = 15) and i is the rank of the estimated
effect when arranged in the ascending order of
magnitude (eg for factor C i = 15)
Figure 2 illustrates the HNPP of the factor
and interaction effects for the helicopter
experiment The computer software package
lsquolsquoDesign-easersquorsquo was used to construct the plot
Those effects which are active and real will
fall off the straight line whereas the inactive
and insignificant effects will fall along the
straight line (Daniel 1959) The figure
reveals that main effects A C E and F are
statistically significant ie paper type wing
length number of clips and wing shape are
statistically significant In order to support
and justify this claim another graphical tool
(main effects plot) is used This shows the
average SNR values at low and high level
settings of each factor Figure 3 illustrates the
main effects plot for the paper helicopter
experiment (using the values from Table V)
This graphical aid provides non-statisticians
with a better picture of the importance of the
effects of the chosen control factors The
slope of the line is an indication of the
importance of a main or interaction effect
The figure shows that the most dominant
factor is the wing length followed by paper
type wing shape and number of clips As each
factor was chosen at two levels the effect of
Table IV SNR table
Trial number SNR Trial number SNR1 893 9 712
2 671 10 595
3 641 11 689
4 662 12 638
5 778 13 901
6 805 14 807
7 1006 15 880
8 795 16 747
Table V Average SNR table
Factors or interactions D C B BD BC F A AB E
SNR 1 781 688 770 763 787 800 812 766 800
SNR 2 746 840 757 765 740 727 715 762 728
Effect estimate plusmn035 152 plusmn013 002 plusmn047 plusmn073 plusmn097 plusmn004 plusmn072
146
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Jiju Antony and Frenie Jiju Antony
Work Study
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832019 Teaching Taguchi Method to IE
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each factor must be assumed to be linear If non-linear effects are to be studied it is
necessary to choose more than two levels for
each factor However it is good practice to
start off an experiment with two levels and
then perform smaller sequential experiments
at higher levels to gain a better understanding
of the nature of the process
For this experiment none of the interaction
effects is significant Consider for example
the interaction between the body length and
body width In order to compute thisinteraction the first step is to compute the
average SNR values at each of the four
combinations of the factor levels Table VI
shows the average SNR values for these four
combinations
An interaction plot is useful in providing a
rapid understanding of the nature of
interactions (Schmidt and Launsby 1992)
Interaction plots are constructed by plotting
the average response values (in this case SNR
values) at each factor level combination
Parallel lines are an indication of the absenceof interaction between the factors whereas
non-parallel lines are an indication of the
presence of interaction between the factors
Figure 4 shows that the effect of body width
on the flight time at both levels of body length
is the same In other words the effect of body
width on the flight time is the same
irrespective of the level of body length This
implies the absence of interaction between
these two factors
Determination of the optimal controlfactor settings
The selection of optimal settings depends on
the objective of the experiment or the nature
of the problem under study For the
helicopter example the objective was to
maximise the flight time In Taguchi
experiments the objective is to identify the
factor settings which yield the highest SNR ndash
these settings will generally produce a
consistent and reliable product Moreover
the process which produces the product will
Figure 2 Half-normal plot of effects
Figure 3 Main effects plot of the control factors
Table VI Average SNR values
Body le ngth Body widt h Aver age SNR
1 1 787
1 2 754
2 1 776
2 2 739
Figure 4 Interaction plot between body length and body width
147
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 89
be insensitive to various sources of
uncontrollable variation For the paper
helicopter experiment the optimal control
factor settings based on the highest SNR have
been determined These are shown in Table
VII In order to decide which level is better for
maximising flight time the SNR values at
both low (level 1) and high (level 2) levels of
each factor are compared
Once the optimal settings are established it
is useful to undertake a confirmation trial
before onward actions are undertaken
(Antony 1996) Three helicopters were made
using the optimal factor settings and the
average flight time was recorded as 356
seconds This shows an improvement of
above 30 per cent on the average flight time
using the range of variable settings The
results also reveal that flight time increases for
larger wing length and smaller body length
Summary and conclusions
The experiment was carried out with the aim
of optimising the flight time of a paper
helicopter In order to study the effect of
variables and the possible interactions
between them in a minimum number of trials
the Taguchi approach to experimental design
was adopted As the experiment itself was
simple the students found it to be a clear
illustration of the process of
defining the problem
identifying the control variables and
possible interactions
defining the required levels for each
variablefactor
determining the response of interest
selecting the most suitable orthogonal
array
performing the experiment
undertaking the analysis andinterpreting the results to obtain a better
understanding of the situation under
review
The Taguchi method is a powerful
approach to address process variability and
optimisation problems However the
application of SDOE and Tm by the
engineering fraternity in UK organisations
is limited due in part to a shortage of skills
in problem solving and inadequate
statistical knowledge This paper
demonstrates a simple means of introducing
students to this powerful tool The
approach uses a simple paper helicopter
experiment For simplicity all control
parameters were studied at two levels This
mirrors actual practice ndash in most
optimisation problems factors at two levelsare the most widely used (Gunst and
Mason 1991 Lucas 1992) The paper
helicopter experiment is quite old and has
been widely used by many statisticians for
teaching purposes However this approach
has focused on minimal statistical jargon
and number crunching and on the use of
modern graphical tools to achieve a rapid
understanding of the results from the
statistical analysis The authors strongly
believe that the experiment provides a
simple and beneficial way to help engineers
approach experimental design in a way that
ensures it is transferrable to their own work
environment
References
Antony J (1996) ``A strategic methodology to the use of
advanced statistical quality control techniquesrsquorsquo
PhD thesisAntony J (1998) ``Some key things industrial engineers
should know about experimental designrsquorsquo Logistics
Information Management 1998 Vol 11 No 6
pp 386-92
Antony J et al (1996) ``Optimisation of core tube life
using Taguchi experimental design methodologyrsquorsquo
Journal of Quality World (Technical Supplement)
IQA March pp 42-50Antony J et al (1998a) ``A strategic methodology to the
use of advanced statistical quality improvement
techniquesrsquorsquo The TQM Magazine (The International
Bi-Monthly for TQM) Vol 10 No 3 pp 169-176
Antony J et al (1998b) ``Key interactionsrsquorsquo Journal of Manufacturing Engineer IEE Vol 77 No 3
pp 136-8
Antony J et al (1999) Experimental Quality plusmn A Strategic
Approach to Achieve and Improve Quality Kluwer
Academic Publishers Dordrecht December
Bendell A (Ed) (1989) Taguchi Methods Applications in World Industry IFS Publications Bedford
Daniel C (1959) ``Use of half-normal plots in interpreting
factorial two level experimentsrsquorsquo Technometrics
Vol 1 No 4 pp 53-70
Table VII Optimal control factor settings
Control factors Optimum level
Paper type Regular (level 1)
Body length 8cm (level 1)
Wing length 12cm (level 2)Body width 2cm (level 1)
Number of clips 1 (level 1)
Wing shape Flat (level 1)
148
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 99
Gunst RF and Mason RL (1991) How to Construct Fractional Factorial Experiments ASQC Statistics
Division ASQC Press Milwaukee MI
Lucas JM (1992) ``Split plotting and randomisation inindustrial experimentsrsquorsquo ASQC Quality Congress
Transactions Nashville TN pp 374-82Morrison JM (1997) ``Statistical engineering plusmn the keyto qualityrsquorsquo Engineering Science and Education
Journal pp 123-7Phadke MS (1989) Quality Engineering using Robust
Design Prentice-Hall International Englewood
Cliffs NJ
Ross PJ (1988) Taguchi Techniques for Quality Engineering McGraw-Hill Publishers New York NY
Rowlands H Antony J and Knowles G (2000) ``An
application of experimental design for processoptimisationrsquorsquo The TQM Magazine Vol 12 No2
pp 78-83Schmidt SR and Launsby RG (1992) Understanding Industrial Designed Experiments Air Academy
Press Washington DCTaguchi G (1986) Introduction to Quality
Engineering Asian Productivity Organisation
Tokyo
Appendix
Table AI Coded design matrix of an L16 (21 5
) orthogonal array
Column
Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2
3 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2
4 1 1 1 2 2 2 2 2 2 2 2 1 1 1 1
5 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2
6 1 2 2 1 1 2 2 2 2 1 1 2 2 1 1
7 1 2 2 2 2 1 1 1 1 2 2 2 2 1 1
8 1 2 2 2 2 1 1 2 2 1 1 1 1 2 2
9 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
10 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1
11 2 1 2 2 1 2 1 1 2 1 2 2 1 2 1
12 2 1 2 2 1 2 1 2 1 2 1 1 2 1 2
13 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1
14 2 2 1 1 2 2 1 2 1 1 2 2 1 2 1
15 2 2 1 2 1 1 2 1 2 2 1 2 1 1 2
16 2 2 1 2 1 1 2 2 1 1 2 1 2 2 1
149
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
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Step1 formulation of the problem ndash the
success of any experiment is dependent
on a full understanding of the nature of
the problem
Step 2 identification of the output
performance characteristics m ost relevant
to the problemStep 3 identification of control factors
noise factors and signal factors (if any)
Control factors are those which can be
controlled under normal production
conditions Noise factors are those which
are either too difficult or too expensive to
control under normal production
conditions Signal factors are those which
affect the mean performance of the
process
Step 4 selection of factor levels possibleinteractions and the degrees of freedom
associated with each factor and the
interaction effects
Step 5 design of an appropriate
orthogonal array (OA)
Step 6 preparation of the experiment
Step 7 running of the experiment with
appropriate data collection
Step 8 statistical analysis and
interpretation of experimental results
Step 9 undertaking a confirmatory run of the experiment
Paper helicopter experiment
In many academic institutions within the UK
the focus of engineering statistics is on the
theory of probability (for example card
shuffling dice rolling etc) the mathematical
aspects of probability and probability
distributions (eg normal exponentialbinomial Poisson log-normal etc)
hypothesis tests etc Quality improvement
techniques (DOE Tm SPC etc) are often
not covered Understandably graduates are
not confident about using such techniques at
their place of work
As part of an exercise to increase the
awareness of Tm amongst industrial
engineers the authors used a simple paper
helicopter experiment readily used in
academic institutions Due to a limitedamount of time one member from each
group in the class was involved with the
experimental work However the students
were all asked to analyse and interpret the
data (on an individual basis) The results of
the analysis were discussed in the classroom
as part of the process of gaining an
understanding of experimental objectives and
process
The paper helicopter experiment is quite
well known among engineers and statisticians
in both the academic and industrial worldsMany industrial training programmes on Tm
use it in some form However they often focus
on the design and analysis of the experiment
without providing guidance to engineers on
the interpretation of results from the analysis
Moreover many courses do not cover the
importance of careful experimental planning
for the success of any industrially designed
experiment
The purpose of this experiment was to
provide undergraduate engineering studentswith an understanding of the role of
Taguchirsquos lsquolsquoparameter designrsquorsquo (sometimes
called lsquolsquorobust designrsquorsquo) in tackling both
product and process quality-related problems
in real-life situations Parameter design is a
well established methodology for improving
product and process quality at minimal cost
by reducing the effect of undesirable external
influences which cause variation in product or
process performance (Phadke 1989)
The objective of the exercise was to identifythe optimal settings of control factors which
would maximise the flight time of paper
helicopters (with minimum variation) Here
control factors refer to those which can be
easily controlled and varied by the designer or
operator in normal production conditions A
brainstorming session by a group of students
identified six control factors which were
thought to influence the time of flight (refer to
Table II) Brainstorming should be
considered an integral part of the Taguchimethodology ndash it is a useful technique in
identifying the most influential factors in an
experiment
In order to simplify the experiment each
factor was studied at two levels The lsquolsquolevelrsquorsquo
of a factor here refers to the specified value of
Table II Control factors and their range of settings for the experiment
Control factor Labels Level 1 Level 2
Paper type A Regular Bond
Body length B 8cm 12cm
Wing length C 8cm 12cm
Body width D 2cm 3cm
Number of clips E 1 2
Wing shape F Flat Angled
143
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 49
a setting For example in the experiment
body width was studied at 2cm and 3cm
Factors at three (and higher) levels make
analysis more complicated ndash and are therefore
not used in awareness-raising sessions
Having identified the control factors it is
important to list the interactions which are to
be studied for the experiment Interaction
exists when the effect of one factor is not the
same at different levels of the other factor An
effect refers to the change in response due to
the change in level of a factor (Antony et al
1998b) Consider for example the factors
wing length and body length of the paper
helicopter Assume each factor was kept attwo-levels for the study Time of flight is the
response (or quality characteristic) of interest
Interaction between wing length and body
length exists when the effect of wing length on
time of flight at two different levels of body
length is different
For this experiment three interactions were
identified (from the brainstorming session) as
being of interest(1) body length pound wing length (B pound C or
BC)
(2) body length pound body width (B pound D or
BD) and
(3) paper type pound body length (A pound B or AB)
The following noise factors were identified (as
having some impact on the flight time but
being difficult to control)
operator-to-operator variationdraughts
reaction time and
ground surface
One aim was to determine the control factor
settings which would best dampen the effect
of these noise factors According to Taguchi
there is an optimal combination of factor
settings which counters the effects of noise In
order to minimise the effect of these noise
factors the same student was responsible for
all timings ndash reducing the effects of variable
reaction times when hitting the stopwatch
upon release of the helicopter and its hitting
the ground
Figure 1 illustrates a template for the model
of a paper helicopter which can be made from
an A4 size paper It forms the basis of a simple
experiment requiring only simple items such
as paper scissors and paper clips It takesabout six hours to design the experiment
collect the data and then perform the
statistical analysis (with the lsquolsquoexperimentrsquorsquo
itself taking about 90 minutes) In this case
the statistical analysis was executed as a
homework assignment though the results
were discussed in the classroom in detail
Choice of orthogonal array design
The choice of a suitable orthogonal array
(OA) design is critical for the success of an
experiment and depends on the total degrees
of freedom required to study the main and
interaction effects the goal of the experiment
resources and budget available and time
constraints Orthogonal arrays allow one to
compute the main and interaction effects via a
minimum number of experimental trials(Ross 1988) lsquolsquoDegrees of freedomrsquorsquo refers to
the number of fair and independent
comparisons that can be made from a set of
observations In the context of SDOE the
number of degrees of freedom is one less than
the number of levels associated with the
factor In other words the number of degrees
of freedom associated with a factor at p-levels
is ( p-1) As the number of degrees of freedom
associated with a factor at two levels is unity
in the present example the number of degrees
of freedom for studying the six main effects is
equal to six The number of degrees of
freedom associated with an interaction is the
product of the number of degrees of freedom
associated with each main effect involved in
the interaction (Antony 1998) In this simple
case the number of degrees of freedom for
studying the three interaction effects is equalto three Therefore the total degrees of
freedom is equal to nine (ie 6 + 3) It is
important to notice that the number of
Figure 1 Template for paper helicopter design
144
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 59
experimental trials must be greater than the
total degrees of freedom required for studying
the effects The standard OAs for factors with
two levels are L 4 L 8 L 1 6 L 32 and so on Here
the notation lsquolsquoLrsquorsquo implies that the information
is based on the Latin square arrangement of
factors A Latin square arrangement is a
square matrix arrangement of factors with
separable factor effects Here the numbers 4
8 12 16 etc denote the number of
experimental trials For the helicopter
experiment as the total degrees of freedom is
equal to nine the closest number of
experimental trials that can be employed for
the experiment is 16 (ie L 1 6 OA) Having
identified the most suitable OA the next step
was to assign the main and interaction effects
to various columns of the array A standard
L 16 OA (see Appendix) contains 15 columns
for either studying 15 main effects or a
combination of main and interaction effects
so that the degrees of freedom will add up to
15 In the present example there are only six
main and three interaction effects Thismeans that only nine columns out of 15 are
used For example factor D (refer to Table
III) was assigned to column 1 and factor C to
column 2 Column 3 is empty (see Table III)
as the interaction between these factors was of
no interest in this experiment Using the
standard linear graphs and OA (Ross 1988)
the remaining factors and interactions were
assigned to the columns of an L 1 6 in the
following manner
Column 1 ndash body width (D) column 2 ndash
wing length (C) column 4 ndash body length (B)
column 5 ndash body width pound body length (B poundD) column 6 ndash wing length pound body length (B
poundC) column 7 ndash wing shape (F) column 8 ndash
paper type (A) column 12 ndash body length poundpaper type (AB) and column 14 ndash number of
clips (E)
The experimental layout showing all the
factors and interactions along with the flight
times (measured in seconds) is shown in
Table III As each factor was studied at two
levels coded level 1 represents the low level of
a factor setting and level 2 represents the high
level setting Each experiment was replicated
in order to capture variation in results due to
uncontrolled noise
Statistical analysis and interpretation ofresults
In Taguchirsquos parameter design the basic
objective is to identify the conditions whichoptimise processproduct performance In
arriving at this optimal set of conditions
Taguchi advocates the use of signal-to-noise
ratio (SNR) ndash the need is to maximise the
performance of a system or product by
minimising the effect of noise while
maximising the mean performance The SNR
is treated as a response (output) of the
experiment which is a measure of variation
when uncontrolled noise factors are present in
Table III Experimental layout
Column no 1 2 4 5 6 7 8 12 14
Factorsinteractions D C B BD BC F A AB E Flight time
Trial no
1 1 1 1 1 1 1 1 1 1 276 283
2 1 1 1 1 1 1 2 2 2 220 213
3 1 1 2 2 2 2 1 2 2 193 230
4 1 1 2 2 2 2 2 1 1 219 210
5 1 2 1 1 2 2 1 1 2 240 250
6 1 2 1 1 2 2 2 2 1 282 231
7 1 2 2 2 1 1 1 2 1 339 301
8 1 2 2 2 1 1 2 1 2 262 239
9 2 1 1 2 1 2 1 1 1 246 212
10 2 1 1 2 1 2 2 2 2 208 190
11 2 1 2 1 2 1 1 2 2 214 229
12 2 1 2 1 2 1 2 1 1 205 212
13 2 2 1 2 2 1 1 1 2 296 27014 2 2 1 2 2 1 2 2 1 247 260
15 2 2 2 1 1 2 1 2 1 262 291
16 2 2 2 1 1 2 2 1 2 232 241
145
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 69
the system (Antony et al 1999) Taguchi has
developed and defined over 60 different
SNRs for engineering applications of
parameter design For the present study as
the objective was to maximise time of flight it
was decided to select the SNR related to
larger-the-better (LTB) qualitycharacteristics This is generally used for
quality characteristics such as strength fuel
efficiency process yield life of a component
and so on For LTB quality characteristics
the SNR is given by the following equation
SNR ˆ iexcl10logpound 1
ncurren
1
y2i
currenhellip1dagger
where n = number of values at each trial
condition (ie 2 from Table II) and yi = each
observed valueTable IV illustrates the SNR values (based
on equation 1) corresponding to each trial
condition
Table V illustrates the average SNR values
(SNR) at low (level 1) and high (level 2) levels
and the effect of each main and interaction
effect on the SNR
Sample calculation for factor lsquolsquoCrsquorsquo
Average SNR at level 1 of factor lsquolsquoCrsquorsquo =
SNRC 2 = 18 [893 + 671 + 641 + 662
+712 + 595 + 689 + 638]
= 688
Similarly average SNR at level 2 of factor
lsquolsquoCrsquorsquo = SNRC 2 = 18 [778 + 805 + 1006 +
795 + 901 + 807 + 880 + 747]
= 840
Effect = SNRC 2 - SNRC 1
= 840 - 688 = 152
The other main and interaction effects were
calculated in a similar manner (see Table V)
Having obtained the average SNR values
the next step is the identification of significant
main and interaction effects which influence
the SNR To achieve this a powerful
graphical tool called half-normal probabilityplots (HNPP) is useful
A half-normal probability plot (HNPP) is
obtained by plotting the absolute values of the
effects (both main andor interaction effects)
along the X-axis and the per cent probability
along the Y-axis The per cent probability
can be obtained by using the following
equation
P i ˆhellipi iexcl 0
5dagger
npound 100 hellip2dagger
where n = number of estimated effects
(n = 15) and i is the rank of the estimated
effect when arranged in the ascending order of
magnitude (eg for factor C i = 15)
Figure 2 illustrates the HNPP of the factor
and interaction effects for the helicopter
experiment The computer software package
lsquolsquoDesign-easersquorsquo was used to construct the plot
Those effects which are active and real will
fall off the straight line whereas the inactive
and insignificant effects will fall along the
straight line (Daniel 1959) The figure
reveals that main effects A C E and F are
statistically significant ie paper type wing
length number of clips and wing shape are
statistically significant In order to support
and justify this claim another graphical tool
(main effects plot) is used This shows the
average SNR values at low and high level
settings of each factor Figure 3 illustrates the
main effects plot for the paper helicopter
experiment (using the values from Table V)
This graphical aid provides non-statisticians
with a better picture of the importance of the
effects of the chosen control factors The
slope of the line is an indication of the
importance of a main or interaction effect
The figure shows that the most dominant
factor is the wing length followed by paper
type wing shape and number of clips As each
factor was chosen at two levels the effect of
Table IV SNR table
Trial number SNR Trial number SNR1 893 9 712
2 671 10 595
3 641 11 689
4 662 12 638
5 778 13 901
6 805 14 807
7 1006 15 880
8 795 16 747
Table V Average SNR table
Factors or interactions D C B BD BC F A AB E
SNR 1 781 688 770 763 787 800 812 766 800
SNR 2 746 840 757 765 740 727 715 762 728
Effect estimate plusmn035 152 plusmn013 002 plusmn047 plusmn073 plusmn097 plusmn004 plusmn072
146
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 79
each factor must be assumed to be linear If non-linear effects are to be studied it is
necessary to choose more than two levels for
each factor However it is good practice to
start off an experiment with two levels and
then perform smaller sequential experiments
at higher levels to gain a better understanding
of the nature of the process
For this experiment none of the interaction
effects is significant Consider for example
the interaction between the body length and
body width In order to compute thisinteraction the first step is to compute the
average SNR values at each of the four
combinations of the factor levels Table VI
shows the average SNR values for these four
combinations
An interaction plot is useful in providing a
rapid understanding of the nature of
interactions (Schmidt and Launsby 1992)
Interaction plots are constructed by plotting
the average response values (in this case SNR
values) at each factor level combination
Parallel lines are an indication of the absenceof interaction between the factors whereas
non-parallel lines are an indication of the
presence of interaction between the factors
Figure 4 shows that the effect of body width
on the flight time at both levels of body length
is the same In other words the effect of body
width on the flight time is the same
irrespective of the level of body length This
implies the absence of interaction between
these two factors
Determination of the optimal controlfactor settings
The selection of optimal settings depends on
the objective of the experiment or the nature
of the problem under study For the
helicopter example the objective was to
maximise the flight time In Taguchi
experiments the objective is to identify the
factor settings which yield the highest SNR ndash
these settings will generally produce a
consistent and reliable product Moreover
the process which produces the product will
Figure 2 Half-normal plot of effects
Figure 3 Main effects plot of the control factors
Table VI Average SNR values
Body le ngth Body widt h Aver age SNR
1 1 787
1 2 754
2 1 776
2 2 739
Figure 4 Interaction plot between body length and body width
147
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 89
be insensitive to various sources of
uncontrollable variation For the paper
helicopter experiment the optimal control
factor settings based on the highest SNR have
been determined These are shown in Table
VII In order to decide which level is better for
maximising flight time the SNR values at
both low (level 1) and high (level 2) levels of
each factor are compared
Once the optimal settings are established it
is useful to undertake a confirmation trial
before onward actions are undertaken
(Antony 1996) Three helicopters were made
using the optimal factor settings and the
average flight time was recorded as 356
seconds This shows an improvement of
above 30 per cent on the average flight time
using the range of variable settings The
results also reveal that flight time increases for
larger wing length and smaller body length
Summary and conclusions
The experiment was carried out with the aim
of optimising the flight time of a paper
helicopter In order to study the effect of
variables and the possible interactions
between them in a minimum number of trials
the Taguchi approach to experimental design
was adopted As the experiment itself was
simple the students found it to be a clear
illustration of the process of
defining the problem
identifying the control variables and
possible interactions
defining the required levels for each
variablefactor
determining the response of interest
selecting the most suitable orthogonal
array
performing the experiment
undertaking the analysis andinterpreting the results to obtain a better
understanding of the situation under
review
The Taguchi method is a powerful
approach to address process variability and
optimisation problems However the
application of SDOE and Tm by the
engineering fraternity in UK organisations
is limited due in part to a shortage of skills
in problem solving and inadequate
statistical knowledge This paper
demonstrates a simple means of introducing
students to this powerful tool The
approach uses a simple paper helicopter
experiment For simplicity all control
parameters were studied at two levels This
mirrors actual practice ndash in most
optimisation problems factors at two levelsare the most widely used (Gunst and
Mason 1991 Lucas 1992) The paper
helicopter experiment is quite old and has
been widely used by many statisticians for
teaching purposes However this approach
has focused on minimal statistical jargon
and number crunching and on the use of
modern graphical tools to achieve a rapid
understanding of the results from the
statistical analysis The authors strongly
believe that the experiment provides a
simple and beneficial way to help engineers
approach experimental design in a way that
ensures it is transferrable to their own work
environment
References
Antony J (1996) ``A strategic methodology to the use of
advanced statistical quality control techniquesrsquorsquo
PhD thesisAntony J (1998) ``Some key things industrial engineers
should know about experimental designrsquorsquo Logistics
Information Management 1998 Vol 11 No 6
pp 386-92
Antony J et al (1996) ``Optimisation of core tube life
using Taguchi experimental design methodologyrsquorsquo
Journal of Quality World (Technical Supplement)
IQA March pp 42-50Antony J et al (1998a) ``A strategic methodology to the
use of advanced statistical quality improvement
techniquesrsquorsquo The TQM Magazine (The International
Bi-Monthly for TQM) Vol 10 No 3 pp 169-176
Antony J et al (1998b) ``Key interactionsrsquorsquo Journal of Manufacturing Engineer IEE Vol 77 No 3
pp 136-8
Antony J et al (1999) Experimental Quality plusmn A Strategic
Approach to Achieve and Improve Quality Kluwer
Academic Publishers Dordrecht December
Bendell A (Ed) (1989) Taguchi Methods Applications in World Industry IFS Publications Bedford
Daniel C (1959) ``Use of half-normal plots in interpreting
factorial two level experimentsrsquorsquo Technometrics
Vol 1 No 4 pp 53-70
Table VII Optimal control factor settings
Control factors Optimum level
Paper type Regular (level 1)
Body length 8cm (level 1)
Wing length 12cm (level 2)Body width 2cm (level 1)
Number of clips 1 (level 1)
Wing shape Flat (level 1)
148
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 99
Gunst RF and Mason RL (1991) How to Construct Fractional Factorial Experiments ASQC Statistics
Division ASQC Press Milwaukee MI
Lucas JM (1992) ``Split plotting and randomisation inindustrial experimentsrsquorsquo ASQC Quality Congress
Transactions Nashville TN pp 374-82Morrison JM (1997) ``Statistical engineering plusmn the keyto qualityrsquorsquo Engineering Science and Education
Journal pp 123-7Phadke MS (1989) Quality Engineering using Robust
Design Prentice-Hall International Englewood
Cliffs NJ
Ross PJ (1988) Taguchi Techniques for Quality Engineering McGraw-Hill Publishers New York NY
Rowlands H Antony J and Knowles G (2000) ``An
application of experimental design for processoptimisationrsquorsquo The TQM Magazine Vol 12 No2
pp 78-83Schmidt SR and Launsby RG (1992) Understanding Industrial Designed Experiments Air Academy
Press Washington DCTaguchi G (1986) Introduction to Quality
Engineering Asian Productivity Organisation
Tokyo
Appendix
Table AI Coded design matrix of an L16 (21 5
) orthogonal array
Column
Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2
3 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2
4 1 1 1 2 2 2 2 2 2 2 2 1 1 1 1
5 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2
6 1 2 2 1 1 2 2 2 2 1 1 2 2 1 1
7 1 2 2 2 2 1 1 1 1 2 2 2 2 1 1
8 1 2 2 2 2 1 1 2 2 1 1 1 1 2 2
9 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
10 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1
11 2 1 2 2 1 2 1 1 2 1 2 2 1 2 1
12 2 1 2 2 1 2 1 2 1 2 1 1 2 1 2
13 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1
14 2 2 1 1 2 2 1 2 1 1 2 2 1 2 1
15 2 2 1 2 1 1 2 1 2 2 1 2 1 1 2
16 2 2 1 2 1 1 2 2 1 1 2 1 2 2 1
149
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 49
a setting For example in the experiment
body width was studied at 2cm and 3cm
Factors at three (and higher) levels make
analysis more complicated ndash and are therefore
not used in awareness-raising sessions
Having identified the control factors it is
important to list the interactions which are to
be studied for the experiment Interaction
exists when the effect of one factor is not the
same at different levels of the other factor An
effect refers to the change in response due to
the change in level of a factor (Antony et al
1998b) Consider for example the factors
wing length and body length of the paper
helicopter Assume each factor was kept attwo-levels for the study Time of flight is the
response (or quality characteristic) of interest
Interaction between wing length and body
length exists when the effect of wing length on
time of flight at two different levels of body
length is different
For this experiment three interactions were
identified (from the brainstorming session) as
being of interest(1) body length pound wing length (B pound C or
BC)
(2) body length pound body width (B pound D or
BD) and
(3) paper type pound body length (A pound B or AB)
The following noise factors were identified (as
having some impact on the flight time but
being difficult to control)
operator-to-operator variationdraughts
reaction time and
ground surface
One aim was to determine the control factor
settings which would best dampen the effect
of these noise factors According to Taguchi
there is an optimal combination of factor
settings which counters the effects of noise In
order to minimise the effect of these noise
factors the same student was responsible for
all timings ndash reducing the effects of variable
reaction times when hitting the stopwatch
upon release of the helicopter and its hitting
the ground
Figure 1 illustrates a template for the model
of a paper helicopter which can be made from
an A4 size paper It forms the basis of a simple
experiment requiring only simple items such
as paper scissors and paper clips It takesabout six hours to design the experiment
collect the data and then perform the
statistical analysis (with the lsquolsquoexperimentrsquorsquo
itself taking about 90 minutes) In this case
the statistical analysis was executed as a
homework assignment though the results
were discussed in the classroom in detail
Choice of orthogonal array design
The choice of a suitable orthogonal array
(OA) design is critical for the success of an
experiment and depends on the total degrees
of freedom required to study the main and
interaction effects the goal of the experiment
resources and budget available and time
constraints Orthogonal arrays allow one to
compute the main and interaction effects via a
minimum number of experimental trials(Ross 1988) lsquolsquoDegrees of freedomrsquorsquo refers to
the number of fair and independent
comparisons that can be made from a set of
observations In the context of SDOE the
number of degrees of freedom is one less than
the number of levels associated with the
factor In other words the number of degrees
of freedom associated with a factor at p-levels
is ( p-1) As the number of degrees of freedom
associated with a factor at two levels is unity
in the present example the number of degrees
of freedom for studying the six main effects is
equal to six The number of degrees of
freedom associated with an interaction is the
product of the number of degrees of freedom
associated with each main effect involved in
the interaction (Antony 1998) In this simple
case the number of degrees of freedom for
studying the three interaction effects is equalto three Therefore the total degrees of
freedom is equal to nine (ie 6 + 3) It is
important to notice that the number of
Figure 1 Template for paper helicopter design
144
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 59
experimental trials must be greater than the
total degrees of freedom required for studying
the effects The standard OAs for factors with
two levels are L 4 L 8 L 1 6 L 32 and so on Here
the notation lsquolsquoLrsquorsquo implies that the information
is based on the Latin square arrangement of
factors A Latin square arrangement is a
square matrix arrangement of factors with
separable factor effects Here the numbers 4
8 12 16 etc denote the number of
experimental trials For the helicopter
experiment as the total degrees of freedom is
equal to nine the closest number of
experimental trials that can be employed for
the experiment is 16 (ie L 1 6 OA) Having
identified the most suitable OA the next step
was to assign the main and interaction effects
to various columns of the array A standard
L 16 OA (see Appendix) contains 15 columns
for either studying 15 main effects or a
combination of main and interaction effects
so that the degrees of freedom will add up to
15 In the present example there are only six
main and three interaction effects Thismeans that only nine columns out of 15 are
used For example factor D (refer to Table
III) was assigned to column 1 and factor C to
column 2 Column 3 is empty (see Table III)
as the interaction between these factors was of
no interest in this experiment Using the
standard linear graphs and OA (Ross 1988)
the remaining factors and interactions were
assigned to the columns of an L 1 6 in the
following manner
Column 1 ndash body width (D) column 2 ndash
wing length (C) column 4 ndash body length (B)
column 5 ndash body width pound body length (B poundD) column 6 ndash wing length pound body length (B
poundC) column 7 ndash wing shape (F) column 8 ndash
paper type (A) column 12 ndash body length poundpaper type (AB) and column 14 ndash number of
clips (E)
The experimental layout showing all the
factors and interactions along with the flight
times (measured in seconds) is shown in
Table III As each factor was studied at two
levels coded level 1 represents the low level of
a factor setting and level 2 represents the high
level setting Each experiment was replicated
in order to capture variation in results due to
uncontrolled noise
Statistical analysis and interpretation ofresults
In Taguchirsquos parameter design the basic
objective is to identify the conditions whichoptimise processproduct performance In
arriving at this optimal set of conditions
Taguchi advocates the use of signal-to-noise
ratio (SNR) ndash the need is to maximise the
performance of a system or product by
minimising the effect of noise while
maximising the mean performance The SNR
is treated as a response (output) of the
experiment which is a measure of variation
when uncontrolled noise factors are present in
Table III Experimental layout
Column no 1 2 4 5 6 7 8 12 14
Factorsinteractions D C B BD BC F A AB E Flight time
Trial no
1 1 1 1 1 1 1 1 1 1 276 283
2 1 1 1 1 1 1 2 2 2 220 213
3 1 1 2 2 2 2 1 2 2 193 230
4 1 1 2 2 2 2 2 1 1 219 210
5 1 2 1 1 2 2 1 1 2 240 250
6 1 2 1 1 2 2 2 2 1 282 231
7 1 2 2 2 1 1 1 2 1 339 301
8 1 2 2 2 1 1 2 1 2 262 239
9 2 1 1 2 1 2 1 1 1 246 212
10 2 1 1 2 1 2 2 2 2 208 190
11 2 1 2 1 2 1 1 2 2 214 229
12 2 1 2 1 2 1 2 1 1 205 212
13 2 2 1 2 2 1 1 1 2 296 27014 2 2 1 2 2 1 2 2 1 247 260
15 2 2 2 1 1 2 1 2 1 262 291
16 2 2 2 1 1 2 2 1 2 232 241
145
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 69
the system (Antony et al 1999) Taguchi has
developed and defined over 60 different
SNRs for engineering applications of
parameter design For the present study as
the objective was to maximise time of flight it
was decided to select the SNR related to
larger-the-better (LTB) qualitycharacteristics This is generally used for
quality characteristics such as strength fuel
efficiency process yield life of a component
and so on For LTB quality characteristics
the SNR is given by the following equation
SNR ˆ iexcl10logpound 1
ncurren
1
y2i
currenhellip1dagger
where n = number of values at each trial
condition (ie 2 from Table II) and yi = each
observed valueTable IV illustrates the SNR values (based
on equation 1) corresponding to each trial
condition
Table V illustrates the average SNR values
(SNR) at low (level 1) and high (level 2) levels
and the effect of each main and interaction
effect on the SNR
Sample calculation for factor lsquolsquoCrsquorsquo
Average SNR at level 1 of factor lsquolsquoCrsquorsquo =
SNRC 2 = 18 [893 + 671 + 641 + 662
+712 + 595 + 689 + 638]
= 688
Similarly average SNR at level 2 of factor
lsquolsquoCrsquorsquo = SNRC 2 = 18 [778 + 805 + 1006 +
795 + 901 + 807 + 880 + 747]
= 840
Effect = SNRC 2 - SNRC 1
= 840 - 688 = 152
The other main and interaction effects were
calculated in a similar manner (see Table V)
Having obtained the average SNR values
the next step is the identification of significant
main and interaction effects which influence
the SNR To achieve this a powerful
graphical tool called half-normal probabilityplots (HNPP) is useful
A half-normal probability plot (HNPP) is
obtained by plotting the absolute values of the
effects (both main andor interaction effects)
along the X-axis and the per cent probability
along the Y-axis The per cent probability
can be obtained by using the following
equation
P i ˆhellipi iexcl 0
5dagger
npound 100 hellip2dagger
where n = number of estimated effects
(n = 15) and i is the rank of the estimated
effect when arranged in the ascending order of
magnitude (eg for factor C i = 15)
Figure 2 illustrates the HNPP of the factor
and interaction effects for the helicopter
experiment The computer software package
lsquolsquoDesign-easersquorsquo was used to construct the plot
Those effects which are active and real will
fall off the straight line whereas the inactive
and insignificant effects will fall along the
straight line (Daniel 1959) The figure
reveals that main effects A C E and F are
statistically significant ie paper type wing
length number of clips and wing shape are
statistically significant In order to support
and justify this claim another graphical tool
(main effects plot) is used This shows the
average SNR values at low and high level
settings of each factor Figure 3 illustrates the
main effects plot for the paper helicopter
experiment (using the values from Table V)
This graphical aid provides non-statisticians
with a better picture of the importance of the
effects of the chosen control factors The
slope of the line is an indication of the
importance of a main or interaction effect
The figure shows that the most dominant
factor is the wing length followed by paper
type wing shape and number of clips As each
factor was chosen at two levels the effect of
Table IV SNR table
Trial number SNR Trial number SNR1 893 9 712
2 671 10 595
3 641 11 689
4 662 12 638
5 778 13 901
6 805 14 807
7 1006 15 880
8 795 16 747
Table V Average SNR table
Factors or interactions D C B BD BC F A AB E
SNR 1 781 688 770 763 787 800 812 766 800
SNR 2 746 840 757 765 740 727 715 762 728
Effect estimate plusmn035 152 plusmn013 002 plusmn047 plusmn073 plusmn097 plusmn004 plusmn072
146
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 79
each factor must be assumed to be linear If non-linear effects are to be studied it is
necessary to choose more than two levels for
each factor However it is good practice to
start off an experiment with two levels and
then perform smaller sequential experiments
at higher levels to gain a better understanding
of the nature of the process
For this experiment none of the interaction
effects is significant Consider for example
the interaction between the body length and
body width In order to compute thisinteraction the first step is to compute the
average SNR values at each of the four
combinations of the factor levels Table VI
shows the average SNR values for these four
combinations
An interaction plot is useful in providing a
rapid understanding of the nature of
interactions (Schmidt and Launsby 1992)
Interaction plots are constructed by plotting
the average response values (in this case SNR
values) at each factor level combination
Parallel lines are an indication of the absenceof interaction between the factors whereas
non-parallel lines are an indication of the
presence of interaction between the factors
Figure 4 shows that the effect of body width
on the flight time at both levels of body length
is the same In other words the effect of body
width on the flight time is the same
irrespective of the level of body length This
implies the absence of interaction between
these two factors
Determination of the optimal controlfactor settings
The selection of optimal settings depends on
the objective of the experiment or the nature
of the problem under study For the
helicopter example the objective was to
maximise the flight time In Taguchi
experiments the objective is to identify the
factor settings which yield the highest SNR ndash
these settings will generally produce a
consistent and reliable product Moreover
the process which produces the product will
Figure 2 Half-normal plot of effects
Figure 3 Main effects plot of the control factors
Table VI Average SNR values
Body le ngth Body widt h Aver age SNR
1 1 787
1 2 754
2 1 776
2 2 739
Figure 4 Interaction plot between body length and body width
147
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 89
be insensitive to various sources of
uncontrollable variation For the paper
helicopter experiment the optimal control
factor settings based on the highest SNR have
been determined These are shown in Table
VII In order to decide which level is better for
maximising flight time the SNR values at
both low (level 1) and high (level 2) levels of
each factor are compared
Once the optimal settings are established it
is useful to undertake a confirmation trial
before onward actions are undertaken
(Antony 1996) Three helicopters were made
using the optimal factor settings and the
average flight time was recorded as 356
seconds This shows an improvement of
above 30 per cent on the average flight time
using the range of variable settings The
results also reveal that flight time increases for
larger wing length and smaller body length
Summary and conclusions
The experiment was carried out with the aim
of optimising the flight time of a paper
helicopter In order to study the effect of
variables and the possible interactions
between them in a minimum number of trials
the Taguchi approach to experimental design
was adopted As the experiment itself was
simple the students found it to be a clear
illustration of the process of
defining the problem
identifying the control variables and
possible interactions
defining the required levels for each
variablefactor
determining the response of interest
selecting the most suitable orthogonal
array
performing the experiment
undertaking the analysis andinterpreting the results to obtain a better
understanding of the situation under
review
The Taguchi method is a powerful
approach to address process variability and
optimisation problems However the
application of SDOE and Tm by the
engineering fraternity in UK organisations
is limited due in part to a shortage of skills
in problem solving and inadequate
statistical knowledge This paper
demonstrates a simple means of introducing
students to this powerful tool The
approach uses a simple paper helicopter
experiment For simplicity all control
parameters were studied at two levels This
mirrors actual practice ndash in most
optimisation problems factors at two levelsare the most widely used (Gunst and
Mason 1991 Lucas 1992) The paper
helicopter experiment is quite old and has
been widely used by many statisticians for
teaching purposes However this approach
has focused on minimal statistical jargon
and number crunching and on the use of
modern graphical tools to achieve a rapid
understanding of the results from the
statistical analysis The authors strongly
believe that the experiment provides a
simple and beneficial way to help engineers
approach experimental design in a way that
ensures it is transferrable to their own work
environment
References
Antony J (1996) ``A strategic methodology to the use of
advanced statistical quality control techniquesrsquorsquo
PhD thesisAntony J (1998) ``Some key things industrial engineers
should know about experimental designrsquorsquo Logistics
Information Management 1998 Vol 11 No 6
pp 386-92
Antony J et al (1996) ``Optimisation of core tube life
using Taguchi experimental design methodologyrsquorsquo
Journal of Quality World (Technical Supplement)
IQA March pp 42-50Antony J et al (1998a) ``A strategic methodology to the
use of advanced statistical quality improvement
techniquesrsquorsquo The TQM Magazine (The International
Bi-Monthly for TQM) Vol 10 No 3 pp 169-176
Antony J et al (1998b) ``Key interactionsrsquorsquo Journal of Manufacturing Engineer IEE Vol 77 No 3
pp 136-8
Antony J et al (1999) Experimental Quality plusmn A Strategic
Approach to Achieve and Improve Quality Kluwer
Academic Publishers Dordrecht December
Bendell A (Ed) (1989) Taguchi Methods Applications in World Industry IFS Publications Bedford
Daniel C (1959) ``Use of half-normal plots in interpreting
factorial two level experimentsrsquorsquo Technometrics
Vol 1 No 4 pp 53-70
Table VII Optimal control factor settings
Control factors Optimum level
Paper type Regular (level 1)
Body length 8cm (level 1)
Wing length 12cm (level 2)Body width 2cm (level 1)
Number of clips 1 (level 1)
Wing shape Flat (level 1)
148
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 99
Gunst RF and Mason RL (1991) How to Construct Fractional Factorial Experiments ASQC Statistics
Division ASQC Press Milwaukee MI
Lucas JM (1992) ``Split plotting and randomisation inindustrial experimentsrsquorsquo ASQC Quality Congress
Transactions Nashville TN pp 374-82Morrison JM (1997) ``Statistical engineering plusmn the keyto qualityrsquorsquo Engineering Science and Education
Journal pp 123-7Phadke MS (1989) Quality Engineering using Robust
Design Prentice-Hall International Englewood
Cliffs NJ
Ross PJ (1988) Taguchi Techniques for Quality Engineering McGraw-Hill Publishers New York NY
Rowlands H Antony J and Knowles G (2000) ``An
application of experimental design for processoptimisationrsquorsquo The TQM Magazine Vol 12 No2
pp 78-83Schmidt SR and Launsby RG (1992) Understanding Industrial Designed Experiments Air Academy
Press Washington DCTaguchi G (1986) Introduction to Quality
Engineering Asian Productivity Organisation
Tokyo
Appendix
Table AI Coded design matrix of an L16 (21 5
) orthogonal array
Column
Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2
3 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2
4 1 1 1 2 2 2 2 2 2 2 2 1 1 1 1
5 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2
6 1 2 2 1 1 2 2 2 2 1 1 2 2 1 1
7 1 2 2 2 2 1 1 1 1 2 2 2 2 1 1
8 1 2 2 2 2 1 1 2 2 1 1 1 1 2 2
9 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
10 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1
11 2 1 2 2 1 2 1 1 2 1 2 2 1 2 1
12 2 1 2 2 1 2 1 2 1 2 1 1 2 1 2
13 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1
14 2 2 1 1 2 2 1 2 1 1 2 2 1 2 1
15 2 2 1 2 1 1 2 1 2 2 1 2 1 1 2
16 2 2 1 2 1 1 2 2 1 1 2 1 2 2 1
149
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 59
experimental trials must be greater than the
total degrees of freedom required for studying
the effects The standard OAs for factors with
two levels are L 4 L 8 L 1 6 L 32 and so on Here
the notation lsquolsquoLrsquorsquo implies that the information
is based on the Latin square arrangement of
factors A Latin square arrangement is a
square matrix arrangement of factors with
separable factor effects Here the numbers 4
8 12 16 etc denote the number of
experimental trials For the helicopter
experiment as the total degrees of freedom is
equal to nine the closest number of
experimental trials that can be employed for
the experiment is 16 (ie L 1 6 OA) Having
identified the most suitable OA the next step
was to assign the main and interaction effects
to various columns of the array A standard
L 16 OA (see Appendix) contains 15 columns
for either studying 15 main effects or a
combination of main and interaction effects
so that the degrees of freedom will add up to
15 In the present example there are only six
main and three interaction effects Thismeans that only nine columns out of 15 are
used For example factor D (refer to Table
III) was assigned to column 1 and factor C to
column 2 Column 3 is empty (see Table III)
as the interaction between these factors was of
no interest in this experiment Using the
standard linear graphs and OA (Ross 1988)
the remaining factors and interactions were
assigned to the columns of an L 1 6 in the
following manner
Column 1 ndash body width (D) column 2 ndash
wing length (C) column 4 ndash body length (B)
column 5 ndash body width pound body length (B poundD) column 6 ndash wing length pound body length (B
poundC) column 7 ndash wing shape (F) column 8 ndash
paper type (A) column 12 ndash body length poundpaper type (AB) and column 14 ndash number of
clips (E)
The experimental layout showing all the
factors and interactions along with the flight
times (measured in seconds) is shown in
Table III As each factor was studied at two
levels coded level 1 represents the low level of
a factor setting and level 2 represents the high
level setting Each experiment was replicated
in order to capture variation in results due to
uncontrolled noise
Statistical analysis and interpretation ofresults
In Taguchirsquos parameter design the basic
objective is to identify the conditions whichoptimise processproduct performance In
arriving at this optimal set of conditions
Taguchi advocates the use of signal-to-noise
ratio (SNR) ndash the need is to maximise the
performance of a system or product by
minimising the effect of noise while
maximising the mean performance The SNR
is treated as a response (output) of the
experiment which is a measure of variation
when uncontrolled noise factors are present in
Table III Experimental layout
Column no 1 2 4 5 6 7 8 12 14
Factorsinteractions D C B BD BC F A AB E Flight time
Trial no
1 1 1 1 1 1 1 1 1 1 276 283
2 1 1 1 1 1 1 2 2 2 220 213
3 1 1 2 2 2 2 1 2 2 193 230
4 1 1 2 2 2 2 2 1 1 219 210
5 1 2 1 1 2 2 1 1 2 240 250
6 1 2 1 1 2 2 2 2 1 282 231
7 1 2 2 2 1 1 1 2 1 339 301
8 1 2 2 2 1 1 2 1 2 262 239
9 2 1 1 2 1 2 1 1 1 246 212
10 2 1 1 2 1 2 2 2 2 208 190
11 2 1 2 1 2 1 1 2 2 214 229
12 2 1 2 1 2 1 2 1 1 205 212
13 2 2 1 2 2 1 1 1 2 296 27014 2 2 1 2 2 1 2 2 1 247 260
15 2 2 2 1 1 2 1 2 1 262 291
16 2 2 2 1 1 2 2 1 2 232 241
145
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 69
the system (Antony et al 1999) Taguchi has
developed and defined over 60 different
SNRs for engineering applications of
parameter design For the present study as
the objective was to maximise time of flight it
was decided to select the SNR related to
larger-the-better (LTB) qualitycharacteristics This is generally used for
quality characteristics such as strength fuel
efficiency process yield life of a component
and so on For LTB quality characteristics
the SNR is given by the following equation
SNR ˆ iexcl10logpound 1
ncurren
1
y2i
currenhellip1dagger
where n = number of values at each trial
condition (ie 2 from Table II) and yi = each
observed valueTable IV illustrates the SNR values (based
on equation 1) corresponding to each trial
condition
Table V illustrates the average SNR values
(SNR) at low (level 1) and high (level 2) levels
and the effect of each main and interaction
effect on the SNR
Sample calculation for factor lsquolsquoCrsquorsquo
Average SNR at level 1 of factor lsquolsquoCrsquorsquo =
SNRC 2 = 18 [893 + 671 + 641 + 662
+712 + 595 + 689 + 638]
= 688
Similarly average SNR at level 2 of factor
lsquolsquoCrsquorsquo = SNRC 2 = 18 [778 + 805 + 1006 +
795 + 901 + 807 + 880 + 747]
= 840
Effect = SNRC 2 - SNRC 1
= 840 - 688 = 152
The other main and interaction effects were
calculated in a similar manner (see Table V)
Having obtained the average SNR values
the next step is the identification of significant
main and interaction effects which influence
the SNR To achieve this a powerful
graphical tool called half-normal probabilityplots (HNPP) is useful
A half-normal probability plot (HNPP) is
obtained by plotting the absolute values of the
effects (both main andor interaction effects)
along the X-axis and the per cent probability
along the Y-axis The per cent probability
can be obtained by using the following
equation
P i ˆhellipi iexcl 0
5dagger
npound 100 hellip2dagger
where n = number of estimated effects
(n = 15) and i is the rank of the estimated
effect when arranged in the ascending order of
magnitude (eg for factor C i = 15)
Figure 2 illustrates the HNPP of the factor
and interaction effects for the helicopter
experiment The computer software package
lsquolsquoDesign-easersquorsquo was used to construct the plot
Those effects which are active and real will
fall off the straight line whereas the inactive
and insignificant effects will fall along the
straight line (Daniel 1959) The figure
reveals that main effects A C E and F are
statistically significant ie paper type wing
length number of clips and wing shape are
statistically significant In order to support
and justify this claim another graphical tool
(main effects plot) is used This shows the
average SNR values at low and high level
settings of each factor Figure 3 illustrates the
main effects plot for the paper helicopter
experiment (using the values from Table V)
This graphical aid provides non-statisticians
with a better picture of the importance of the
effects of the chosen control factors The
slope of the line is an indication of the
importance of a main or interaction effect
The figure shows that the most dominant
factor is the wing length followed by paper
type wing shape and number of clips As each
factor was chosen at two levels the effect of
Table IV SNR table
Trial number SNR Trial number SNR1 893 9 712
2 671 10 595
3 641 11 689
4 662 12 638
5 778 13 901
6 805 14 807
7 1006 15 880
8 795 16 747
Table V Average SNR table
Factors or interactions D C B BD BC F A AB E
SNR 1 781 688 770 763 787 800 812 766 800
SNR 2 746 840 757 765 740 727 715 762 728
Effect estimate plusmn035 152 plusmn013 002 plusmn047 plusmn073 plusmn097 plusmn004 plusmn072
146
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 79
each factor must be assumed to be linear If non-linear effects are to be studied it is
necessary to choose more than two levels for
each factor However it is good practice to
start off an experiment with two levels and
then perform smaller sequential experiments
at higher levels to gain a better understanding
of the nature of the process
For this experiment none of the interaction
effects is significant Consider for example
the interaction between the body length and
body width In order to compute thisinteraction the first step is to compute the
average SNR values at each of the four
combinations of the factor levels Table VI
shows the average SNR values for these four
combinations
An interaction plot is useful in providing a
rapid understanding of the nature of
interactions (Schmidt and Launsby 1992)
Interaction plots are constructed by plotting
the average response values (in this case SNR
values) at each factor level combination
Parallel lines are an indication of the absenceof interaction between the factors whereas
non-parallel lines are an indication of the
presence of interaction between the factors
Figure 4 shows that the effect of body width
on the flight time at both levels of body length
is the same In other words the effect of body
width on the flight time is the same
irrespective of the level of body length This
implies the absence of interaction between
these two factors
Determination of the optimal controlfactor settings
The selection of optimal settings depends on
the objective of the experiment or the nature
of the problem under study For the
helicopter example the objective was to
maximise the flight time In Taguchi
experiments the objective is to identify the
factor settings which yield the highest SNR ndash
these settings will generally produce a
consistent and reliable product Moreover
the process which produces the product will
Figure 2 Half-normal plot of effects
Figure 3 Main effects plot of the control factors
Table VI Average SNR values
Body le ngth Body widt h Aver age SNR
1 1 787
1 2 754
2 1 776
2 2 739
Figure 4 Interaction plot between body length and body width
147
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 89
be insensitive to various sources of
uncontrollable variation For the paper
helicopter experiment the optimal control
factor settings based on the highest SNR have
been determined These are shown in Table
VII In order to decide which level is better for
maximising flight time the SNR values at
both low (level 1) and high (level 2) levels of
each factor are compared
Once the optimal settings are established it
is useful to undertake a confirmation trial
before onward actions are undertaken
(Antony 1996) Three helicopters were made
using the optimal factor settings and the
average flight time was recorded as 356
seconds This shows an improvement of
above 30 per cent on the average flight time
using the range of variable settings The
results also reveal that flight time increases for
larger wing length and smaller body length
Summary and conclusions
The experiment was carried out with the aim
of optimising the flight time of a paper
helicopter In order to study the effect of
variables and the possible interactions
between them in a minimum number of trials
the Taguchi approach to experimental design
was adopted As the experiment itself was
simple the students found it to be a clear
illustration of the process of
defining the problem
identifying the control variables and
possible interactions
defining the required levels for each
variablefactor
determining the response of interest
selecting the most suitable orthogonal
array
performing the experiment
undertaking the analysis andinterpreting the results to obtain a better
understanding of the situation under
review
The Taguchi method is a powerful
approach to address process variability and
optimisation problems However the
application of SDOE and Tm by the
engineering fraternity in UK organisations
is limited due in part to a shortage of skills
in problem solving and inadequate
statistical knowledge This paper
demonstrates a simple means of introducing
students to this powerful tool The
approach uses a simple paper helicopter
experiment For simplicity all control
parameters were studied at two levels This
mirrors actual practice ndash in most
optimisation problems factors at two levelsare the most widely used (Gunst and
Mason 1991 Lucas 1992) The paper
helicopter experiment is quite old and has
been widely used by many statisticians for
teaching purposes However this approach
has focused on minimal statistical jargon
and number crunching and on the use of
modern graphical tools to achieve a rapid
understanding of the results from the
statistical analysis The authors strongly
believe that the experiment provides a
simple and beneficial way to help engineers
approach experimental design in a way that
ensures it is transferrable to their own work
environment
References
Antony J (1996) ``A strategic methodology to the use of
advanced statistical quality control techniquesrsquorsquo
PhD thesisAntony J (1998) ``Some key things industrial engineers
should know about experimental designrsquorsquo Logistics
Information Management 1998 Vol 11 No 6
pp 386-92
Antony J et al (1996) ``Optimisation of core tube life
using Taguchi experimental design methodologyrsquorsquo
Journal of Quality World (Technical Supplement)
IQA March pp 42-50Antony J et al (1998a) ``A strategic methodology to the
use of advanced statistical quality improvement
techniquesrsquorsquo The TQM Magazine (The International
Bi-Monthly for TQM) Vol 10 No 3 pp 169-176
Antony J et al (1998b) ``Key interactionsrsquorsquo Journal of Manufacturing Engineer IEE Vol 77 No 3
pp 136-8
Antony J et al (1999) Experimental Quality plusmn A Strategic
Approach to Achieve and Improve Quality Kluwer
Academic Publishers Dordrecht December
Bendell A (Ed) (1989) Taguchi Methods Applications in World Industry IFS Publications Bedford
Daniel C (1959) ``Use of half-normal plots in interpreting
factorial two level experimentsrsquorsquo Technometrics
Vol 1 No 4 pp 53-70
Table VII Optimal control factor settings
Control factors Optimum level
Paper type Regular (level 1)
Body length 8cm (level 1)
Wing length 12cm (level 2)Body width 2cm (level 1)
Number of clips 1 (level 1)
Wing shape Flat (level 1)
148
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 99
Gunst RF and Mason RL (1991) How to Construct Fractional Factorial Experiments ASQC Statistics
Division ASQC Press Milwaukee MI
Lucas JM (1992) ``Split plotting and randomisation inindustrial experimentsrsquorsquo ASQC Quality Congress
Transactions Nashville TN pp 374-82Morrison JM (1997) ``Statistical engineering plusmn the keyto qualityrsquorsquo Engineering Science and Education
Journal pp 123-7Phadke MS (1989) Quality Engineering using Robust
Design Prentice-Hall International Englewood
Cliffs NJ
Ross PJ (1988) Taguchi Techniques for Quality Engineering McGraw-Hill Publishers New York NY
Rowlands H Antony J and Knowles G (2000) ``An
application of experimental design for processoptimisationrsquorsquo The TQM Magazine Vol 12 No2
pp 78-83Schmidt SR and Launsby RG (1992) Understanding Industrial Designed Experiments Air Academy
Press Washington DCTaguchi G (1986) Introduction to Quality
Engineering Asian Productivity Organisation
Tokyo
Appendix
Table AI Coded design matrix of an L16 (21 5
) orthogonal array
Column
Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2
3 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2
4 1 1 1 2 2 2 2 2 2 2 2 1 1 1 1
5 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2
6 1 2 2 1 1 2 2 2 2 1 1 2 2 1 1
7 1 2 2 2 2 1 1 1 1 2 2 2 2 1 1
8 1 2 2 2 2 1 1 2 2 1 1 1 1 2 2
9 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
10 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1
11 2 1 2 2 1 2 1 1 2 1 2 2 1 2 1
12 2 1 2 2 1 2 1 2 1 2 1 1 2 1 2
13 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1
14 2 2 1 1 2 2 1 2 1 1 2 2 1 2 1
15 2 2 1 2 1 1 2 1 2 2 1 2 1 1 2
16 2 2 1 2 1 1 2 2 1 1 2 1 2 2 1
149
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 69
the system (Antony et al 1999) Taguchi has
developed and defined over 60 different
SNRs for engineering applications of
parameter design For the present study as
the objective was to maximise time of flight it
was decided to select the SNR related to
larger-the-better (LTB) qualitycharacteristics This is generally used for
quality characteristics such as strength fuel
efficiency process yield life of a component
and so on For LTB quality characteristics
the SNR is given by the following equation
SNR ˆ iexcl10logpound 1
ncurren
1
y2i
currenhellip1dagger
where n = number of values at each trial
condition (ie 2 from Table II) and yi = each
observed valueTable IV illustrates the SNR values (based
on equation 1) corresponding to each trial
condition
Table V illustrates the average SNR values
(SNR) at low (level 1) and high (level 2) levels
and the effect of each main and interaction
effect on the SNR
Sample calculation for factor lsquolsquoCrsquorsquo
Average SNR at level 1 of factor lsquolsquoCrsquorsquo =
SNRC 2 = 18 [893 + 671 + 641 + 662
+712 + 595 + 689 + 638]
= 688
Similarly average SNR at level 2 of factor
lsquolsquoCrsquorsquo = SNRC 2 = 18 [778 + 805 + 1006 +
795 + 901 + 807 + 880 + 747]
= 840
Effect = SNRC 2 - SNRC 1
= 840 - 688 = 152
The other main and interaction effects were
calculated in a similar manner (see Table V)
Having obtained the average SNR values
the next step is the identification of significant
main and interaction effects which influence
the SNR To achieve this a powerful
graphical tool called half-normal probabilityplots (HNPP) is useful
A half-normal probability plot (HNPP) is
obtained by plotting the absolute values of the
effects (both main andor interaction effects)
along the X-axis and the per cent probability
along the Y-axis The per cent probability
can be obtained by using the following
equation
P i ˆhellipi iexcl 0
5dagger
npound 100 hellip2dagger
where n = number of estimated effects
(n = 15) and i is the rank of the estimated
effect when arranged in the ascending order of
magnitude (eg for factor C i = 15)
Figure 2 illustrates the HNPP of the factor
and interaction effects for the helicopter
experiment The computer software package
lsquolsquoDesign-easersquorsquo was used to construct the plot
Those effects which are active and real will
fall off the straight line whereas the inactive
and insignificant effects will fall along the
straight line (Daniel 1959) The figure
reveals that main effects A C E and F are
statistically significant ie paper type wing
length number of clips and wing shape are
statistically significant In order to support
and justify this claim another graphical tool
(main effects plot) is used This shows the
average SNR values at low and high level
settings of each factor Figure 3 illustrates the
main effects plot for the paper helicopter
experiment (using the values from Table V)
This graphical aid provides non-statisticians
with a better picture of the importance of the
effects of the chosen control factors The
slope of the line is an indication of the
importance of a main or interaction effect
The figure shows that the most dominant
factor is the wing length followed by paper
type wing shape and number of clips As each
factor was chosen at two levels the effect of
Table IV SNR table
Trial number SNR Trial number SNR1 893 9 712
2 671 10 595
3 641 11 689
4 662 12 638
5 778 13 901
6 805 14 807
7 1006 15 880
8 795 16 747
Table V Average SNR table
Factors or interactions D C B BD BC F A AB E
SNR 1 781 688 770 763 787 800 812 766 800
SNR 2 746 840 757 765 740 727 715 762 728
Effect estimate plusmn035 152 plusmn013 002 plusmn047 plusmn073 plusmn097 plusmn004 plusmn072
146
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 79
each factor must be assumed to be linear If non-linear effects are to be studied it is
necessary to choose more than two levels for
each factor However it is good practice to
start off an experiment with two levels and
then perform smaller sequential experiments
at higher levels to gain a better understanding
of the nature of the process
For this experiment none of the interaction
effects is significant Consider for example
the interaction between the body length and
body width In order to compute thisinteraction the first step is to compute the
average SNR values at each of the four
combinations of the factor levels Table VI
shows the average SNR values for these four
combinations
An interaction plot is useful in providing a
rapid understanding of the nature of
interactions (Schmidt and Launsby 1992)
Interaction plots are constructed by plotting
the average response values (in this case SNR
values) at each factor level combination
Parallel lines are an indication of the absenceof interaction between the factors whereas
non-parallel lines are an indication of the
presence of interaction between the factors
Figure 4 shows that the effect of body width
on the flight time at both levels of body length
is the same In other words the effect of body
width on the flight time is the same
irrespective of the level of body length This
implies the absence of interaction between
these two factors
Determination of the optimal controlfactor settings
The selection of optimal settings depends on
the objective of the experiment or the nature
of the problem under study For the
helicopter example the objective was to
maximise the flight time In Taguchi
experiments the objective is to identify the
factor settings which yield the highest SNR ndash
these settings will generally produce a
consistent and reliable product Moreover
the process which produces the product will
Figure 2 Half-normal plot of effects
Figure 3 Main effects plot of the control factors
Table VI Average SNR values
Body le ngth Body widt h Aver age SNR
1 1 787
1 2 754
2 1 776
2 2 739
Figure 4 Interaction plot between body length and body width
147
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 89
be insensitive to various sources of
uncontrollable variation For the paper
helicopter experiment the optimal control
factor settings based on the highest SNR have
been determined These are shown in Table
VII In order to decide which level is better for
maximising flight time the SNR values at
both low (level 1) and high (level 2) levels of
each factor are compared
Once the optimal settings are established it
is useful to undertake a confirmation trial
before onward actions are undertaken
(Antony 1996) Three helicopters were made
using the optimal factor settings and the
average flight time was recorded as 356
seconds This shows an improvement of
above 30 per cent on the average flight time
using the range of variable settings The
results also reveal that flight time increases for
larger wing length and smaller body length
Summary and conclusions
The experiment was carried out with the aim
of optimising the flight time of a paper
helicopter In order to study the effect of
variables and the possible interactions
between them in a minimum number of trials
the Taguchi approach to experimental design
was adopted As the experiment itself was
simple the students found it to be a clear
illustration of the process of
defining the problem
identifying the control variables and
possible interactions
defining the required levels for each
variablefactor
determining the response of interest
selecting the most suitable orthogonal
array
performing the experiment
undertaking the analysis andinterpreting the results to obtain a better
understanding of the situation under
review
The Taguchi method is a powerful
approach to address process variability and
optimisation problems However the
application of SDOE and Tm by the
engineering fraternity in UK organisations
is limited due in part to a shortage of skills
in problem solving and inadequate
statistical knowledge This paper
demonstrates a simple means of introducing
students to this powerful tool The
approach uses a simple paper helicopter
experiment For simplicity all control
parameters were studied at two levels This
mirrors actual practice ndash in most
optimisation problems factors at two levelsare the most widely used (Gunst and
Mason 1991 Lucas 1992) The paper
helicopter experiment is quite old and has
been widely used by many statisticians for
teaching purposes However this approach
has focused on minimal statistical jargon
and number crunching and on the use of
modern graphical tools to achieve a rapid
understanding of the results from the
statistical analysis The authors strongly
believe that the experiment provides a
simple and beneficial way to help engineers
approach experimental design in a way that
ensures it is transferrable to their own work
environment
References
Antony J (1996) ``A strategic methodology to the use of
advanced statistical quality control techniquesrsquorsquo
PhD thesisAntony J (1998) ``Some key things industrial engineers
should know about experimental designrsquorsquo Logistics
Information Management 1998 Vol 11 No 6
pp 386-92
Antony J et al (1996) ``Optimisation of core tube life
using Taguchi experimental design methodologyrsquorsquo
Journal of Quality World (Technical Supplement)
IQA March pp 42-50Antony J et al (1998a) ``A strategic methodology to the
use of advanced statistical quality improvement
techniquesrsquorsquo The TQM Magazine (The International
Bi-Monthly for TQM) Vol 10 No 3 pp 169-176
Antony J et al (1998b) ``Key interactionsrsquorsquo Journal of Manufacturing Engineer IEE Vol 77 No 3
pp 136-8
Antony J et al (1999) Experimental Quality plusmn A Strategic
Approach to Achieve and Improve Quality Kluwer
Academic Publishers Dordrecht December
Bendell A (Ed) (1989) Taguchi Methods Applications in World Industry IFS Publications Bedford
Daniel C (1959) ``Use of half-normal plots in interpreting
factorial two level experimentsrsquorsquo Technometrics
Vol 1 No 4 pp 53-70
Table VII Optimal control factor settings
Control factors Optimum level
Paper type Regular (level 1)
Body length 8cm (level 1)
Wing length 12cm (level 2)Body width 2cm (level 1)
Number of clips 1 (level 1)
Wing shape Flat (level 1)
148
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 99
Gunst RF and Mason RL (1991) How to Construct Fractional Factorial Experiments ASQC Statistics
Division ASQC Press Milwaukee MI
Lucas JM (1992) ``Split plotting and randomisation inindustrial experimentsrsquorsquo ASQC Quality Congress
Transactions Nashville TN pp 374-82Morrison JM (1997) ``Statistical engineering plusmn the keyto qualityrsquorsquo Engineering Science and Education
Journal pp 123-7Phadke MS (1989) Quality Engineering using Robust
Design Prentice-Hall International Englewood
Cliffs NJ
Ross PJ (1988) Taguchi Techniques for Quality Engineering McGraw-Hill Publishers New York NY
Rowlands H Antony J and Knowles G (2000) ``An
application of experimental design for processoptimisationrsquorsquo The TQM Magazine Vol 12 No2
pp 78-83Schmidt SR and Launsby RG (1992) Understanding Industrial Designed Experiments Air Academy
Press Washington DCTaguchi G (1986) Introduction to Quality
Engineering Asian Productivity Organisation
Tokyo
Appendix
Table AI Coded design matrix of an L16 (21 5
) orthogonal array
Column
Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2
3 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2
4 1 1 1 2 2 2 2 2 2 2 2 1 1 1 1
5 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2
6 1 2 2 1 1 2 2 2 2 1 1 2 2 1 1
7 1 2 2 2 2 1 1 1 1 2 2 2 2 1 1
8 1 2 2 2 2 1 1 2 2 1 1 1 1 2 2
9 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
10 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1
11 2 1 2 2 1 2 1 1 2 1 2 2 1 2 1
12 2 1 2 2 1 2 1 2 1 2 1 1 2 1 2
13 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1
14 2 2 1 1 2 2 1 2 1 1 2 2 1 2 1
15 2 2 1 2 1 1 2 1 2 2 1 2 1 1 2
16 2 2 1 2 1 1 2 2 1 1 2 1 2 2 1
149
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 79
each factor must be assumed to be linear If non-linear effects are to be studied it is
necessary to choose more than two levels for
each factor However it is good practice to
start off an experiment with two levels and
then perform smaller sequential experiments
at higher levels to gain a better understanding
of the nature of the process
For this experiment none of the interaction
effects is significant Consider for example
the interaction between the body length and
body width In order to compute thisinteraction the first step is to compute the
average SNR values at each of the four
combinations of the factor levels Table VI
shows the average SNR values for these four
combinations
An interaction plot is useful in providing a
rapid understanding of the nature of
interactions (Schmidt and Launsby 1992)
Interaction plots are constructed by plotting
the average response values (in this case SNR
values) at each factor level combination
Parallel lines are an indication of the absenceof interaction between the factors whereas
non-parallel lines are an indication of the
presence of interaction between the factors
Figure 4 shows that the effect of body width
on the flight time at both levels of body length
is the same In other words the effect of body
width on the flight time is the same
irrespective of the level of body length This
implies the absence of interaction between
these two factors
Determination of the optimal controlfactor settings
The selection of optimal settings depends on
the objective of the experiment or the nature
of the problem under study For the
helicopter example the objective was to
maximise the flight time In Taguchi
experiments the objective is to identify the
factor settings which yield the highest SNR ndash
these settings will generally produce a
consistent and reliable product Moreover
the process which produces the product will
Figure 2 Half-normal plot of effects
Figure 3 Main effects plot of the control factors
Table VI Average SNR values
Body le ngth Body widt h Aver age SNR
1 1 787
1 2 754
2 1 776
2 2 739
Figure 4 Interaction plot between body length and body width
147
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 89
be insensitive to various sources of
uncontrollable variation For the paper
helicopter experiment the optimal control
factor settings based on the highest SNR have
been determined These are shown in Table
VII In order to decide which level is better for
maximising flight time the SNR values at
both low (level 1) and high (level 2) levels of
each factor are compared
Once the optimal settings are established it
is useful to undertake a confirmation trial
before onward actions are undertaken
(Antony 1996) Three helicopters were made
using the optimal factor settings and the
average flight time was recorded as 356
seconds This shows an improvement of
above 30 per cent on the average flight time
using the range of variable settings The
results also reveal that flight time increases for
larger wing length and smaller body length
Summary and conclusions
The experiment was carried out with the aim
of optimising the flight time of a paper
helicopter In order to study the effect of
variables and the possible interactions
between them in a minimum number of trials
the Taguchi approach to experimental design
was adopted As the experiment itself was
simple the students found it to be a clear
illustration of the process of
defining the problem
identifying the control variables and
possible interactions
defining the required levels for each
variablefactor
determining the response of interest
selecting the most suitable orthogonal
array
performing the experiment
undertaking the analysis andinterpreting the results to obtain a better
understanding of the situation under
review
The Taguchi method is a powerful
approach to address process variability and
optimisation problems However the
application of SDOE and Tm by the
engineering fraternity in UK organisations
is limited due in part to a shortage of skills
in problem solving and inadequate
statistical knowledge This paper
demonstrates a simple means of introducing
students to this powerful tool The
approach uses a simple paper helicopter
experiment For simplicity all control
parameters were studied at two levels This
mirrors actual practice ndash in most
optimisation problems factors at two levelsare the most widely used (Gunst and
Mason 1991 Lucas 1992) The paper
helicopter experiment is quite old and has
been widely used by many statisticians for
teaching purposes However this approach
has focused on minimal statistical jargon
and number crunching and on the use of
modern graphical tools to achieve a rapid
understanding of the results from the
statistical analysis The authors strongly
believe that the experiment provides a
simple and beneficial way to help engineers
approach experimental design in a way that
ensures it is transferrable to their own work
environment
References
Antony J (1996) ``A strategic methodology to the use of
advanced statistical quality control techniquesrsquorsquo
PhD thesisAntony J (1998) ``Some key things industrial engineers
should know about experimental designrsquorsquo Logistics
Information Management 1998 Vol 11 No 6
pp 386-92
Antony J et al (1996) ``Optimisation of core tube life
using Taguchi experimental design methodologyrsquorsquo
Journal of Quality World (Technical Supplement)
IQA March pp 42-50Antony J et al (1998a) ``A strategic methodology to the
use of advanced statistical quality improvement
techniquesrsquorsquo The TQM Magazine (The International
Bi-Monthly for TQM) Vol 10 No 3 pp 169-176
Antony J et al (1998b) ``Key interactionsrsquorsquo Journal of Manufacturing Engineer IEE Vol 77 No 3
pp 136-8
Antony J et al (1999) Experimental Quality plusmn A Strategic
Approach to Achieve and Improve Quality Kluwer
Academic Publishers Dordrecht December
Bendell A (Ed) (1989) Taguchi Methods Applications in World Industry IFS Publications Bedford
Daniel C (1959) ``Use of half-normal plots in interpreting
factorial two level experimentsrsquorsquo Technometrics
Vol 1 No 4 pp 53-70
Table VII Optimal control factor settings
Control factors Optimum level
Paper type Regular (level 1)
Body length 8cm (level 1)
Wing length 12cm (level 2)Body width 2cm (level 1)
Number of clips 1 (level 1)
Wing shape Flat (level 1)
148
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 99
Gunst RF and Mason RL (1991) How to Construct Fractional Factorial Experiments ASQC Statistics
Division ASQC Press Milwaukee MI
Lucas JM (1992) ``Split plotting and randomisation inindustrial experimentsrsquorsquo ASQC Quality Congress
Transactions Nashville TN pp 374-82Morrison JM (1997) ``Statistical engineering plusmn the keyto qualityrsquorsquo Engineering Science and Education
Journal pp 123-7Phadke MS (1989) Quality Engineering using Robust
Design Prentice-Hall International Englewood
Cliffs NJ
Ross PJ (1988) Taguchi Techniques for Quality Engineering McGraw-Hill Publishers New York NY
Rowlands H Antony J and Knowles G (2000) ``An
application of experimental design for processoptimisationrsquorsquo The TQM Magazine Vol 12 No2
pp 78-83Schmidt SR and Launsby RG (1992) Understanding Industrial Designed Experiments Air Academy
Press Washington DCTaguchi G (1986) Introduction to Quality
Engineering Asian Productivity Organisation
Tokyo
Appendix
Table AI Coded design matrix of an L16 (21 5
) orthogonal array
Column
Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2
3 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2
4 1 1 1 2 2 2 2 2 2 2 2 1 1 1 1
5 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2
6 1 2 2 1 1 2 2 2 2 1 1 2 2 1 1
7 1 2 2 2 2 1 1 1 1 2 2 2 2 1 1
8 1 2 2 2 2 1 1 2 2 1 1 1 1 2 2
9 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
10 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1
11 2 1 2 2 1 2 1 1 2 1 2 2 1 2 1
12 2 1 2 2 1 2 1 2 1 2 1 1 2 1 2
13 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1
14 2 2 1 1 2 2 1 2 1 1 2 2 1 2 1
15 2 2 1 2 1 1 2 1 2 2 1 2 1 1 2
16 2 2 1 2 1 1 2 2 1 1 2 1 2 2 1
149
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 89
be insensitive to various sources of
uncontrollable variation For the paper
helicopter experiment the optimal control
factor settings based on the highest SNR have
been determined These are shown in Table
VII In order to decide which level is better for
maximising flight time the SNR values at
both low (level 1) and high (level 2) levels of
each factor are compared
Once the optimal settings are established it
is useful to undertake a confirmation trial
before onward actions are undertaken
(Antony 1996) Three helicopters were made
using the optimal factor settings and the
average flight time was recorded as 356
seconds This shows an improvement of
above 30 per cent on the average flight time
using the range of variable settings The
results also reveal that flight time increases for
larger wing length and smaller body length
Summary and conclusions
The experiment was carried out with the aim
of optimising the flight time of a paper
helicopter In order to study the effect of
variables and the possible interactions
between them in a minimum number of trials
the Taguchi approach to experimental design
was adopted As the experiment itself was
simple the students found it to be a clear
illustration of the process of
defining the problem
identifying the control variables and
possible interactions
defining the required levels for each
variablefactor
determining the response of interest
selecting the most suitable orthogonal
array
performing the experiment
undertaking the analysis andinterpreting the results to obtain a better
understanding of the situation under
review
The Taguchi method is a powerful
approach to address process variability and
optimisation problems However the
application of SDOE and Tm by the
engineering fraternity in UK organisations
is limited due in part to a shortage of skills
in problem solving and inadequate
statistical knowledge This paper
demonstrates a simple means of introducing
students to this powerful tool The
approach uses a simple paper helicopter
experiment For simplicity all control
parameters were studied at two levels This
mirrors actual practice ndash in most
optimisation problems factors at two levelsare the most widely used (Gunst and
Mason 1991 Lucas 1992) The paper
helicopter experiment is quite old and has
been widely used by many statisticians for
teaching purposes However this approach
has focused on minimal statistical jargon
and number crunching and on the use of
modern graphical tools to achieve a rapid
understanding of the results from the
statistical analysis The authors strongly
believe that the experiment provides a
simple and beneficial way to help engineers
approach experimental design in a way that
ensures it is transferrable to their own work
environment
References
Antony J (1996) ``A strategic methodology to the use of
advanced statistical quality control techniquesrsquorsquo
PhD thesisAntony J (1998) ``Some key things industrial engineers
should know about experimental designrsquorsquo Logistics
Information Management 1998 Vol 11 No 6
pp 386-92
Antony J et al (1996) ``Optimisation of core tube life
using Taguchi experimental design methodologyrsquorsquo
Journal of Quality World (Technical Supplement)
IQA March pp 42-50Antony J et al (1998a) ``A strategic methodology to the
use of advanced statistical quality improvement
techniquesrsquorsquo The TQM Magazine (The International
Bi-Monthly for TQM) Vol 10 No 3 pp 169-176
Antony J et al (1998b) ``Key interactionsrsquorsquo Journal of Manufacturing Engineer IEE Vol 77 No 3
pp 136-8
Antony J et al (1999) Experimental Quality plusmn A Strategic
Approach to Achieve and Improve Quality Kluwer
Academic Publishers Dordrecht December
Bendell A (Ed) (1989) Taguchi Methods Applications in World Industry IFS Publications Bedford
Daniel C (1959) ``Use of half-normal plots in interpreting
factorial two level experimentsrsquorsquo Technometrics
Vol 1 No 4 pp 53-70
Table VII Optimal control factor settings
Control factors Optimum level
Paper type Regular (level 1)
Body length 8cm (level 1)
Wing length 12cm (level 2)Body width 2cm (level 1)
Number of clips 1 (level 1)
Wing shape Flat (level 1)
148
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 99
Gunst RF and Mason RL (1991) How to Construct Fractional Factorial Experiments ASQC Statistics
Division ASQC Press Milwaukee MI
Lucas JM (1992) ``Split plotting and randomisation inindustrial experimentsrsquorsquo ASQC Quality Congress
Transactions Nashville TN pp 374-82Morrison JM (1997) ``Statistical engineering plusmn the keyto qualityrsquorsquo Engineering Science and Education
Journal pp 123-7Phadke MS (1989) Quality Engineering using Robust
Design Prentice-Hall International Englewood
Cliffs NJ
Ross PJ (1988) Taguchi Techniques for Quality Engineering McGraw-Hill Publishers New York NY
Rowlands H Antony J and Knowles G (2000) ``An
application of experimental design for processoptimisationrsquorsquo The TQM Magazine Vol 12 No2
pp 78-83Schmidt SR and Launsby RG (1992) Understanding Industrial Designed Experiments Air Academy
Press Washington DCTaguchi G (1986) Introduction to Quality
Engineering Asian Productivity Organisation
Tokyo
Appendix
Table AI Coded design matrix of an L16 (21 5
) orthogonal array
Column
Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2
3 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2
4 1 1 1 2 2 2 2 2 2 2 2 1 1 1 1
5 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2
6 1 2 2 1 1 2 2 2 2 1 1 2 2 1 1
7 1 2 2 2 2 1 1 1 1 2 2 2 2 1 1
8 1 2 2 2 2 1 1 2 2 1 1 1 1 2 2
9 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
10 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1
11 2 1 2 2 1 2 1 1 2 1 2 2 1 2 1
12 2 1 2 2 1 2 1 2 1 2 1 1 2 1 2
13 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1
14 2 2 1 1 2 2 1 2 1 1 2 2 1 2 1
15 2 2 1 2 1 1 2 1 2 2 1 2 1 1 2
16 2 2 1 2 1 1 2 2 1 1 2 1 2 2 1
149
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
832019 Teaching Taguchi Method to IE
httpslidepdfcomreaderfullteaching-taguchi-method-to-ie 99
Gunst RF and Mason RL (1991) How to Construct Fractional Factorial Experiments ASQC Statistics
Division ASQC Press Milwaukee MI
Lucas JM (1992) ``Split plotting and randomisation inindustrial experimentsrsquorsquo ASQC Quality Congress
Transactions Nashville TN pp 374-82Morrison JM (1997) ``Statistical engineering plusmn the keyto qualityrsquorsquo Engineering Science and Education
Journal pp 123-7Phadke MS (1989) Quality Engineering using Robust
Design Prentice-Hall International Englewood
Cliffs NJ
Ross PJ (1988) Taguchi Techniques for Quality Engineering McGraw-Hill Publishers New York NY
Rowlands H Antony J and Knowles G (2000) ``An
application of experimental design for processoptimisationrsquorsquo The TQM Magazine Vol 12 No2
pp 78-83Schmidt SR and Launsby RG (1992) Understanding Industrial Designed Experiments Air Academy
Press Washington DCTaguchi G (1986) Introduction to Quality
Engineering Asian Productivity Organisation
Tokyo
Appendix
Table AI Coded design matrix of an L16 (21 5
) orthogonal array
Column
Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2
3 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2
4 1 1 1 2 2 2 2 2 2 2 2 1 1 1 1
5 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2
6 1 2 2 1 1 2 2 2 2 1 1 2 2 1 1
7 1 2 2 2 2 1 1 1 1 2 2 2 2 1 1
8 1 2 2 2 2 1 1 2 2 1 1 1 1 2 2
9 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
10 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1
11 2 1 2 2 1 2 1 1 2 1 2 2 1 2 1
12 2 1 2 2 1 2 1 2 1 2 1 1 2 1 2
13 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1
14 2 2 1 1 2 2 1 2 1 1 2 2 1 2 1
15 2 2 1 2 1 1 2 1 2 2 1 2 1 1 2
16 2 2 1 2 1 1 2 2 1 1 2 1 2 2 1
149
Teaching the Taguchi method to industrial engineers
Jiju Antony and Frenie Jiju Antony
Work Study
Volume 50 Number 4 2001 141plusmn149
