9. design of experiment

QUALITY TOOLS & TECHNIQUES

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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?

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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

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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

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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

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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

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EXPERIMENTS

ONE-FACTOR AT A TIMEEXPRIMENTS

BEST GUESSEXPERIMENTS

FACTORIALEXPERIMENTS

FACTORIAL EXPERIMENTS

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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

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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

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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


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EXAMPLE (Cont…):


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EXAMPLE (Cont…):

Stat > DOE > Factorial > Factorial Plots


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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.


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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.


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EXAMPLE (Cont…):


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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


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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.


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EXAMPLE (Cont…):


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EXAMPLE (Cont…):

Stat > DOE > Factorial > Factorial Plots


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EXAMPLE (Cont…):


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EXAMPLE (Cont…):


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EXAMPLE (Cont…):Stat > DOE > Factorial > Analyze Factorial Design…


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EXAMPLE (Cont…):

GENERAL FULL FACTORIAL DESIGN

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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.”


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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


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Stat DOE Factorial Create Factorial Design…

Define Design


CREATE THE DESIGN

Define Factors / Levels

Randomize Runs


THE PLAN:


Stat DOE Factorial Analyze factorial Design


210-1-2

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Standardized Residual

Perc

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34323028

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Fitted Value

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210-1-2

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Standardized Residual

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50454035302520151051

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Observation Order

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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


Stat DOE Factorial Factorial Plots


350300

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605040

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Temperature

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Operators

Cycel Time

Main Effects Plot for ScoreData Means

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T emperature

Operators

Cycel T ime

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Temperature

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Interaction Plot for ScoreData Means

QUESTIONS

9. design of experiment

Engineering

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