Post on 13-Jan-2017
QUALITY TOOLS & TECHNIQUES
1
TQ TDESIGN OF EXPERIMENT
By: -Hakeem–Ur–Rehman
Certified Six Sigma Black Belt (SQII – Singapore)IRCA (UK) Lead Auditor ISO 9001
MS–Total Quality Management (P.U.)MSc (Information & Operations Management) (P.U.)
IQTM–PU
WHAT IS EXPERIMENT?
2
In statistics, an experiment refers to any process thatgenerates a set of data.
An experiment involves a test or series of test in whichpurposeful changes are made to the input variables of aprocess or system so that changes in the output responsescan be observed and identified.
Noise Factors
OBJECTIVES OF CONDUCTING AN EXPERIMENT
3
1. Determining which variables (Input), X, aremost influential on the response (output), y,in a study.
2. Determining where to set the influential X’sso that ‘y’ is near the nominal requirement.
3. Determining where to set the influential x’s sothat variability in ‘y’ is small.
4. Determining where to set the influential x’s sothat the effects of uncontrollable variables ‘z’are minimized.
TERMINOLOGIES
4
Terms used in Design of Experiments (DOE) need to defined, these are:
RESPONSE: A measurable outcome of interest, e.g.: yield, strength, etc.
FACTORS: Controllable variables that are deliberately manipulated to determine their individual
and joint effects on the response(s), OR Factors are those quantities that affect theoutcome of an experiment, e.g.: temperature, time, etc.
LEVELS: Levels refer to the values of factors for which the data is gathered, “values that factor
will take in an experiment”, e.g.:Level–1 for time = 2hoursLevel–2 for time = 3 hours
TREATEMENT: A set of specified factor levels for an experimental run, e.g.:
Treatment–1: time = 2hrs and temperature = 1750 CTreatment–2: time = 3hrs and temperature = 2250 C
NOISE: Variables that affect product / process performance, whose values cannot be
controlled or are not controlled for economic reasons. REPLICATION:
Replication is a systematic duplication of series of experimental runs. It provides themeans of measuring precision by calculating the experimental error.
EXAMPLES
5
EXAMPLE–1: In a MACHING PROCESS RESPONSE: Surface Finish “Y” FACTORS: Speed of machine “XA” & Depth of
Cut “XB” LEVELS: High & Low
EXAMPLE–2: In a POPCORN MAKING PROCESS RESPONSE: Volume (ml) Yield of Popcorn “Y” FACTORS: Type of Popper “XA” & Grade of
corn used “XB” LEVELS: Air, and Oil & Budget, Regular and
luxury
TYPES OF EXPERIMENTS
6
EXPERIMENTS
ONE-FACTOR AT A TIMEEXPRIMENTS
BEST GUESSEXPERIMENTS
FACTORIALEXPERIMENTS
FACTORIAL EXPERIMENTS
7
Factorial experiment is the CORRECT and MOST EFFICIENT type of experiment in dealingwith several factors involved in a study; Factors are varied together instead of one at time.
The Three Basic Principles of experimental design are:1. Replication2. Randomization3. Blocking
1. REPLICATION: It has two important properties:
Allow us to obtain an estimate of Experimental error which provide a basic unit ofmeasurement for determining whether observed differences in the data are reallyStatistically different.
If sample mean is used to estimate the effect of a factor, then replication allow a moreprecise estimate of the effect.
2. RANDOMIZATION: By randomization, both the allocation of the experimental material and the order of individual
runs or trails can be perform randomly; As statistical methods required observations be independent distributed, randomization made
this assumption valid.
3. BLOCKING: An experiment is arranging the runs of the experiment in groups “Blocks” so that runs within
each block have as much minor variation in common with each other as possible. e.g.: Runs using material from the same lot Runs carried out within a short time frame
2K FACTORIAL
8
2K Factorial Designs are experiments where allFACTORS have only TWO LEVELS
The number of combinations (Runs) for FullFactorial Design is denoted as n = 2k (wherek=number of Factors)
2K
Factors
Levels
22 FACTORIAL EXPERIMENTAL DESIGN
9
EXAMPLE: Consider the manufacture of a product, for use
in the making of paint, in a batch process. Fixed amounts of rawmaterial are heated under pressure in rector-1 for a fixed periodof time and the product is then recovered. Currently the processis operated at temperature 225o C and pressure 4.5 bar. As partof Six Sigma project, aimed at increasing product yield, a 22
factorial experiment with two replications was planned. Yieldsare typically around 90 Kg. It was decided after discussionamongst the project team to use the levels 200o C and 250o Cfor temperature and level 4.0 bar and 5.0 bar for pressure.
RESPONSE: Product Yield “Y” FACTORS: Temperature “XA” & Pressure “XB” LEVELS: 200o C and 250o C & 4.0 bar and 5.0
bar
22 FACTORIAL EXPERIMENTAL DESIGN
10
EXAMPLE (Cont…):
22 FACTORIAL EXPERIMENTAL DESIGN
11
EXAMPLE (Cont…):
Stat > DOE > Factorial > Factorial Plots
22 FACTORIAL EXPERIMENTAL DESIGN
12
EXAMPLE (Cont…):
The Main Effect Plot indicate that: On average, increasing temperature from
200o C to 250o C increases yield ofproduct by 8 kg.
On average, increasing pressure from 4bar to 5 bar decreases yield of product by6Kg.
The parallel lines indicate no temperature–Pressure interaction here.
22 FACTORIAL EXPERIMENTAL DESIGN
13
EXAMPLE (Cont…):Stat > DOE > Factorial > Analyze Factorial Design…
Factorial Fit: Yield versus Temperature, PressureEstimated Effects and Coefficients for Yield (coded units)
Term Effect Coef SE Coef T PConstant 92.000 0.9354 98.35 0.000Temperature 8.000 4.000 0.9354 4.28 0.013Pressure -6.000 -3.000 0.9354 -3.21 0.033Temperature*Pressure 0.000 -0.000 0.9354 -0.00 1.000
S = 2.64575 PRESS = 112R-Sq = 87.72% R-Sq(pred) = 50.88% R-Sq(adj) = 78.51%
The P–Value indicatethat both temperature &pressure have a realeffect on Yield.
22 FACTORIAL EXPERIMENTAL DESIGN
14
EXAMPLE (Cont…):
22 FACTORIAL EXPERIMENTAL DESIGN
15
EXERCISE:
An Engineer desire to study which is the2 Factors determined that affect theDefect Rate in his production line.FACTORS:
Temperature & PressureLEVELS:
Temperature – 60 & 70o C &Pressure – 3.0 & 5.5 BarREPLICATES: 3
DEFECT
3.93183
2.30259
0.0000
2.07944
4.33073
3.33220
2.39790
0.69315
2.19722
2.83321
1.38629
1.38629
23 FACTORIAL EXPERIMENTAL DESIGN
16
EXAMPLE: A plastic manufacturing company had
formed a work improvement company had formed awork improvement team consisting of engineers fromdifferent department. The team objective is to strive toimprove the yield of a coating process. After a series ofbrainstorming session, the team determined that thefollowing are the deciding factors and levels:
A: Temperature: 400o F and 450o FB: Catalyst Con.: 10% and 20%C: Processing Ramp time: 45 seconds and 90
secondsThe design is a 23 factorial and each run (treatment) isreplicated 3 times and total is 24 randomized trial.
23 FACTORIAL EXPERIMENTAL DESIGN
17
EXAMPLE (Cont…):
23 FACTORIAL EXPERIMENTAL DESIGN
18
EXAMPLE (Cont…):
Stat > DOE > Factorial > Factorial Plots
23 FACTORIAL EXPERIMENTAL DESIGN
19
EXAMPLE (Cont…):
23 FACTORIAL EXPERIMENTAL DESIGN
20
EXAMPLE (Cont…):
23 FACTORIAL EXPERIMENTAL DESIGN
21
EXAMPLE (Cont…):Stat > DOE > Factorial > Analyze Factorial Design…
23 FACTORIAL EXPERIMENTAL DESIGN
22
EXAMPLE (Cont…):
GENERAL FULL FACTORIAL DESIGN
23
A design in which at least one factor hasmore than two levels.
The experimental Runs includes allcombination of these factor levels.
Note: “Cube Plot, & Pareto Plot cannot be used in General FullFactorial Design.”
GENERAL FULL FACTORIAL DESIGN
24
Example: Create a General Full Factorial Experiment Where:
FACTORS: Temperature, Operators, and Cycle Time
LEVELS: Temperature: 300 & 350 Operators: 1, 2 & 3 Cycle Time: 40, 50 & 60
Replicate = 3
Response = Score
GENERAL FULL FACTORIAL DESIGN
25
Stat DOE Factorial Create Factorial Design…
Define Design
GENERAL FULL FACTORIAL DESIGN
CREATE THE DESIGN
Define Factors / Levels
Randomize Runs
GENERAL FULL FACTORIAL DESIGN
THE PLAN:
GENERAL FULL FACTORIAL DESIGN
Stat DOE Factorial Analyze factorial Design
GENERAL FULL FACTORIAL DESIGN
210-1-2
99
90
50
10
1
Standardized Residual
Perc
ent
34323028
2
1
0
-1
-2
Fitted Value
Stan
dard
ized
Res
idua
l
210-1-2
10.0
7.5
5.0
2.5
0.0
Standardized Residual
Freq
uenc
y
50454035302520151051
2
1
0
-1
-2
Observation Order
Stan
dard
ized
Res
idua
l
Normal Probability Plot Versus Fits
Histogram Versus Order
Residual Plots for Score
Only temperature is asignificant factor as its P-Value is less than 0.05
GENERAL FULL FACTORIAL DESIGN
Stat DOE Factorial Factorial Plots
GENERAL FULL FACTORIAL DESIGN
350300
32
31
30
321
605040
32
31
30
Temperature
Me
an
Operators
Cycel Time
Main Effects Plot for ScoreData Means
321 605040
32
30
28
32
30
28
T emperature
Operators
Cycel T ime
300
350
Temperature
1
2
3
Operators
Interaction Plot for ScoreData Means
QUESTIONS