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Module-13

DOE (Screening Experiments)


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Design of Experiments - Learning Objectives

At the end of this section delegates will be able to:

Understand the role of Screening Experiments

within the DMAIC Improvement Process

Recognise the differences and advantages of

Fractional Factorial, Full Factorial and One Factorat a Time Experimentation

Analyse and interpret results from Designed

Experiments Understand the purpose of Screening Experiments


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1. Introduction to Design of Experiments

2. Design of Experiments within DMAIC

3. Full Factorial Experiments

4. Fractional Factorial Experiments

5. Screening Experiments6. Designing Screening Experiments

7. Conducting Screening Experiments

8. Screening Experiments Summary

9. Design of Experiments Summary

Design of Experiments - Agenda


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Introduction to Design of Experiments


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Workshop Cooking Part 1


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One Factor at a Time

Advantages

Easy to conduct and analyse

LogicalDisadvantages

Not representative of real conditionsSusceptible to variation

1 1 1 1 1 1 1 1 Result 1

2 2 1 1 1 1 1 1 Result 2

3 2 2 1 1 1 1 1 Result 34 2 2 2 1 1 1 1 Result 4

5 2 2 2 2 1 1 1 Result 5

6 2 2 2 2 2 1 1 Result 6

7 2 2 2 2 2 2 1 Result 7

8 2 2 2 2 2 2 2 Result 8

Run Factors TestNumber A B C D E F G Result


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Full Factorial Experiment

1 1 1 1 1 1 1 1

2 1 1 1 1 1 1 2

3 1 1 1 1 1 2 1

128 2 2 2 2 2 2 2

Run A B C D E F G Result

Advantages Very Good Understanding

Disadvantages Sometimes Impractical & Expensive

4 1 1 1 1 1 2 25 1 1 1 1 2 1 16 1 1 1 1 2 1 27 1 1 1 1 2 2 18 1 1 1 1 2 2 29 1 1 1 2 1 1 110 1 1 1 2 1 1 211 1 1 1 2 1 2 112 1 1 1 2 1 2 2

. . . . . . . .. . . . . . .. . . . . . .

. . . . . . . .

126 2 2 2 2 2 1 2

127 2 2 2 2 2 2 1

.

.


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Panic Mode or Trial & Error

Advantages

Management like the instant response

DisadvantagesAlmost impossible to optimiseConclusions unlikely to be reproducible


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Fractional Factorial

Factor

Run # A B C

1 1 1 1

2 1 2 2

3 2 1 2

4 2 2 1


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Workshop Cooking Part 2


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Design of Experiments

Design of Experiments: Is more efficient than One Factor at a Time or

Trial and Error

Is more robust correct (and statistically valid)conclusions can be drawn

Can be used to estimate interactive effects if

desired


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Design of Experiments within DMAIC


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Reducing Variability of Outputs (ys)

Reducing variability in outputs (ys) is accomplished by:

Determining critical xs (inputs)

Understanding the behaviour of the critical xs howdo they change?

Understanding the effects that the critical xs have onthe ys (outputs)

Establishing controls on the critical xs (inputs) in

order to minimise the variation in the ys (outputs)


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Reducing Variability of Outputs (ys)

Determining critical xs (inputs) this can be accomplished

using DOE and other methodologies

Understanding the behaviour of the critical xs this isusually accomplished using capability studies

Understanding the effects that the critical xs have on the

ys (outputs) this is accomplished using Robust Design,Response Surface Studies and other DOE

Establishing controls on the critical xs (inputs) this is

accomplished using Tolerance Design and Statistical

Process Control (SPC)


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Define ImproveMeasure Control Control Critical xs

Monitor ys

Validate ControlPlan

Close Project

1 5 10 15 20

10.2

10.0

9.8

9.6

Upper Control Limit

Lower Control Limit

y

Phase Review

Analyse Characterise xs

Optimise xs

Set Tolerances for xs

Verify Improvement

15 20 25 30 35

LSL USL

Phase Review

y=f(x1,x2,..)

y

x

. . .. . .

. .. . .. . .

Identify Potential xs

Analyse xs

Select Critical xs

Phase Review

Run 1 2 3 4 5 6 7

1 1 1 1 1 1 1 12 1 1 1 2 2 2 23 1 2 2 1 1 2 2

4 1 2 2 2 2 1 15 2 1 2 1 2 1 26 2 1 2 2 1 2 17 2 2 1 1 2 2 18 2 2 1 2 1 1 2

Effect

C1 C2

C4

C3

C6C5

x

xx

xx

xx

xx

x

x

Select Project

Define ProjectObjective

Form the Team

Map the Process

Identify CustomerRequirements

Identify Priorities

Update Project File

Phase Review

Define Measures (ys)

Evaluate Measurement

System

Determine Process

Stability Determine Process

Capability

Set Targets forMeasures

15 20 25 30 35

LSL USL

Phase Review

DMAIC Improvement Process


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Analyse Phase Flowchart

Critical xs

(Common Causes)

Yes

Variation

Reduction

Issue

Identify

Potential xs

Analyse

xs

Are the xs

Significant?

No

Critical x

(Mistake Proofing)

Yes

Mistake

Proofing

Issue

Identify

Potential xs

Analyse

xs

Are the xs

Significant?

No

Stability

Issue

Identify

Potential xs

Analyse

xs

Are the xs

Significant?

Critical xs

(Special Causes)

Yes

NoScreening

Experimentsand other DOE


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Improve Phase Flowchart Variation Reduction

Categorise Critical xs

(Control & Noise Factors)

Develop Noise Factor Strategy

Select Control Factors & Levels

Design Experiment

Conduct Experiment

Analyse Results

Confirmation Run

Set tolerances for xs

Verify Improvement

(Tolerance Design)

Confirmation

OK?

Project

Objective

Achieved?

Go to Control Phase

Determine Stability

& Capability of Critical xs

Yes

No

No

Yes

Review Project

Robust Design, Response Surface, other DOE


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Full Factorial Experiments


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A full factorial experiment means that every possible

combination of factors and factor levels are tested

It is unlikely that a full factorial will ever be run

during the Analyse Phase of the DMAIC

Full Factorial Experiments


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Three factors (xs) were investigated in this

experiment. The output (y), was the dimension of an

injection moulded part.

Factor

Mould Temperature

Injection Speed

Back Pressure

Levels

Low High

Slow Fast

Small Large

The objective of the experiment was to determine theeffect that the factors (xs) had on the dimension (y)

Moulding Experiment


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2K Experiments

In the moulding experiment 3 factors are being

examined, each at 2 levels

This is referred to as a 23 full factorial experiment

The total number of runs required is 23 = 2 x 2 x 2 = 8

The general nomenclature for 2 level full factorialexperiments is 2k where k = the number of factors

To calculate the number of runs required to conduct a

2 level full factorial we simply calculate 2k


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Run

12

3

4

5

6

7

8

Mould

Temperature

LowHigh

Low

High

Low

High

Low

High

Injection

Speed

SlowSlow

Fast

Fast

Slow

Slow

Fast

Fast

Back

Pressure

LowLow

Low

Low

High

High

High

High

Dimension

(mm)

56.255.6

61.6

52.2

54.0

50.0

60.3

51.1

All combinations of factor levels are investigated

This design is perfectly balanced

Moulding Experiment Layout & Results


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Run

1

2

3

45

6

7

8

Mould

Temperature

-

+

-

+-

+

-

+

Injection

Speed

-

-

+

+-

-

+

+

Back

Pressure

-

-

-

-+

+

+

+

Dimension

(mm)

56.2

55.6

61.6

52.254.0

50.0

60.3

51.1

The convention is to let the symbol indicate the lower

level of the factor.

Moulding Experiment in Coded Form


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Run

12

3

4

5

67

8

Mould

Temperature

-

+

-

+

-

+-

+

Injection

Speed

-

-

+

+

-

-+

+

Back

Pressure

-

-

-

-

+

++

+

Dimension

(mm)

56.2

55.6

61.6

52.2

54.0

50.060.3

51.1

Average for (+) Level

Average for (-) Level

Effect

Mould Temp52.225

58.025

-5.80

Injection Speed56.30

53.95

+2.35

Back Pressure53.85

56.40

-2.55

Effects of the Factors


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Main Effects Plots

MeanofDim

ension(mm)

HighLow

58

56

54

52

HighLow

HighLow

58

56

54

52

A B

C

Main Effects Plot (data means) for Dimension (mm)


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When more than one factor has an effect on the process

output, this does not mean that an interaction exists

between those factors

An interaction exists when the effect a factor has on the

process output depends on the setting of another factor

If there is an interaction between two factors (A and B),then the main effect of Factor A would be different,

dependent on the setting of Factor B

When conducting a full factorial experiment we can

calculate all the possible interactive effects

Interactions


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Interactive effects are investigated by calculating the

average output for each combination of the factors

involved.

For example, if wish to calculate the interactive effect

between mould temperature and injection speed, we need

to calculate the average output at each possible

combination of mould temperature and injection speed.

There are four possible combinations:

Low Mould Temperature with Slow Injection SpeedHigh Mould Temperature with Slow Injection Speed

Low Mould Temperature with Fast Injection Speed

High Mould Temperature with Fast Injection Speed

Calculation of Interactive Effects


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Run

1

2

3

4

56

7

8

Mould

Temperature

Low (-)

High (+)

Low (-)

High (+)

Low (-)High (+)

Low (-)

High (+)

Injection

Speed

Slow (-)

Slow (-)

Fast (+)

Fast (+)

Slow (-)Slow (-)

Fast (+)

Fast (+)

Back

Pressure

Low (-)

Low (-)

Low (-)

Low (-)

High (+)High (+)

High (+)

High (+)

Dimension

(mm)

56.2

55.6

61.6

52.2

54.050.0

60.3

51.1

Low Mould Temperature / Slow Injection Speed = 56.2 & 54.0; Average = 55.10High Mould Temperature / Slow Injection Speed = 55.6 & 50.0; Average = 52.80

Low Mould Temperature / Fast Injection Speed = 61.6 & 60.3 Average = 60.95

High Mould Temperature / Fast Injection Speed = 52.2 & 51.1; Average = 51.65

Mould Temperature x Injection Speed Interaction


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Mould Temperature x Injection Speed

Interaction Measure

51.65 60.95 = -9.3

52.80 55.10 = -2.3

-9.3 (-2.3) = -7.0

-7.0 / 2 = -3.5

Dimension

62 --

61 --

60 --

59 --

58 --

57 --

56 --

55 --

54 --53 --

52 --

51 --

50 --

60.95

52.80

55.10

51.65

Mould Temperature Low (-)

Mould Temperature High (+)

Injection Speed +


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Mould Temperature x Back Pressure

Interaction Measure

50.55 53.90 = -3.35

57.15 58.90 = -1.75

-3.35 (-1.75) = -1.60

-1.60 / 2 = -0.80

Dimension

62 --

61 --

60 --59 --

58 --

57 --

56 --

55 --

54 --

53 --

52 --

51 --

50 --

53.90

57.15

58.90

50.55

Back Pressure Low (-)

Back Pressure High (+)

Mould

Temperature

+


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Injection Speed x Back Pressure

Interaction Measure

55.7 56.9 = -1.2

52.0 55.9 = -3.9

-1.2 (-3.9) = +2.7

2.7 / 2 = +1.35

Dimension

62 --

61 --60 --

59 --

58 --

57 --

56 --

55 --54 --

53 --

52 --

51 --

50 --

56.90

52.00

55.90

55.70

Back Pressure Low (-)

Back Pressure High (+)

Injection Speed +


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Obtain 4 more columns which contain the interactive

effects by multiplying the main effects columns. The effect

of each interaction is then simply the difference between

the average dimension of the +s and the s.

Run

Mould

Temp

Injection

Speed

Back

Pressure MT x IS MT x BP IS x BP MTxISxBP

Dimens.

(mm)

1 - - - + + + - 56.20

2 + - - - - + + 55.60

3 - + - - + - + 61.604 + + - + - - - 52.20

5 - - + + - - + 54.00

6 + - + - + - - 50.00

7 - + + - - + - 60.30

8 + + + + + + + 51.10

Average for + 52.225 56.300 53.850 53.375 54.725 55.800 55.575

Average for - 58.025 53.950 56.400 56.875 55.525 54.450 54.675

Effect -5.80 2.35 -2.55 -3.50 -0.80 1.35 0.90

Another Way of Calculating Effects


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Mould Temperature has the single biggest effect in this

experiment.

The interactive effect between mould temperature and

injection speed is also very important and would have to be

taken into account in any future optimisation activity.

Injection Speed and Back Pressure also merit furtherinvestigation.

We have not tested the statistical significance of the effects at

this stage. In practice we might have taken more data pointswhich would have given us the opportunity to carry out such

tests.

Moulding Experiment - Conclusions


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Minitab Selecting a Design


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Create Factorial Design

Check

Change Number

of factors to 3

Press Designs


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Create Factorial Design - Designs

Select Full Factorial


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Select Factors

C F i l D i F


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Create Factorial Design - Factors

Input:

Factor NamesType

& Levels

C t F t i l D i


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Select Options

C t F t i l D i O ti


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Create Factorial Designs - Options

Uncheckthis

E i t l D i


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Experimental Design

E t Di i D t


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Enter Dimension Data

Data Analysis


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Data Analysis

Analyse Factorial Design


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Analyse Factorial Design

Enter

Dimension

Select

Graphs


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Pareto Chart


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Pareto Chart

Term

Effect

AC

ABC

BC

B

C

AB

A

9876543210

9.357Factor N ame

A Mould Temperature

B Injection Speed

C Back Pressure

Pareto Chart of the Effects(response is Dimension, Alpha = .10)

Lenth's PSE = 3.525

Absolute effect size is

plotted (as in previous

manual calculations)

Session Window Output


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Session Window Output

Analysis of Variance for Dimension (coded units)

Source DF Seq SS Adj SS Adj MS F P

Main Effects 3 91.330 91.330 30.443 * *

2-Way Interactions 3 29.425 29.425 9.808 * *

3-Way Interactions 1 1.620 1.620 1.620 * *

Residual Error 0 * * *

Total 7 122.375

No degrees of freedom to estimate the error, so we

cannot estimate the significance of the factors

Simplifying the Model


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We can estimate the residual error by using the degrees offreedom of some of the least significant terms in the model

Click on Terms in the Analyse Factorial Design dialogue box

in order to remove the chosen terms from the model



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Since the residual error changes each time we remove a term,

it is advisable to take terms out one at a time, starting with the

smallest effect:

Term

Effect

AC

ABC

BC

B

C

AB

A

9876543210

9.357Facto r N ame

A M ould Temperature

B Injection Speed

C Back Pressure

Pareto Chart of the Effects(response is Dimension, Alpha = .10)

Lenth's PSE = 3.525

Highlight term and double click or press

left hand arrow to remove

Revised Pareto Chart & Session Window


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Revised Pareto Chart & Session Window

Term

Standardized Effect

ABC

BC

B

C

AB

A

876543210

6.314Fact or N ame

A M ould Temperature

B Injection Speed

C Back Pressure

Pareto Chart of the Standardized Effects(response is Dimension, Alpha = .10)

Factorial Fit: Dimension versus Mould Temper, Injection Sp, Back Pressur

Estimated Effects and Coefficients for Dimension (coded units)

Term Effect Coef SE Coef T P

Constant 55.125 0.4000 137.81 0.005

Mould Temperature -5.800 -2.900 0.4000 -7.25 0.087

Injection Speed 2.350 1.175 0.4000 2.94 0.209

Back Pressure -2.550 -1.275 0.4000 -3.19 0.194

Mould Temperature*Injection Speed -3.500 -1.750 0.4000 -4.38 0.143

Injection Speed*Back Pressure 1.350 0.675 0.4000 1.69 0.341

Mould Temperature*Injection Speed* 0.900 0.450 0.4000 1.13 0.463

Back Pressure

S = 1.13137 R-Sq = 98.95% R-Sq(adj) = 92.68%



Main Effects 3 91.330 91.330 30.443 23.78 0.149

2-Way Interactions 2 28.145 28.145 14.073 10.99 0.209


Residual Error 1 1.280 1.280 1.280

Total 7 122.375

There is now an error term,

and p values for the remaining

terms. Well now take out the

ABC interaction

Revised Pareto Chart


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Revised Pareto Chart

Term

Standardized Effect

BC

B

C

AB

A

76543210

2.920Factor Name

A Mould Temperature

B Injection Speed

C Back Pressure


Finally we take out the BC interaction

Final Pareto and Session Window Results


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a a eto a d Sess o W dow esu ts

Term

Standardized Effect

B

C

AB

A

6543210

2.353F actor N ame

A M ould T emperature

B Injection Speed

C Back Pressure


Factorial Fit: Dimension versus Mould Temper, Injection Sp, Back Pressur

Estimated Effects and Coefficients for Dimension (coded units)

Term Effect Coef SE Coef T P

Constant 55.125 0.5222 105.56 0.000

Mould Temperature -5.800 -2.900 0.5222 -5.55 0.012

Injection Speed 2.350 1.175 0.5222 2.25 0.110

Back Pressure -2.550 -1.275 0.5222 -2.44 0.092

Mould Temperature*Injection Speed -3.500 -1.750 0.5222 -3.35 0.044

S = 1.47705 R-Sq = 94.65% R-Sq(adj) = 87.52%



Main Effects 3 91.330 91.330 30.443 13.95 0.029


Residual Error 3 6.545 6.545 2.182

Total 7 122.375

Estimated Coefficients for Dimension using data in uncoded units

Term Coef

Constant 55.1250

Mould Temperature -2.90000

Injection Speed 1.17500

Back Pressure -1.27500

Mould Temperature*Injection Speed -1.75000

B, Injection Speed, must stay in

the model as it is involved in the

significant interaction AB

Factorial Plots


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Factorial Plots


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SelectSetup

Checkthese

Factorial Plots


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Move

these

Factors

across

Enter

Dimension

Factorial Plots - Interactions


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Select

Setup

Factorial Plots - Interactions


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Movethese

Factors

across

Enter

Dimension

Main Effects Plots


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Meano

fDimension

HighLow

58

56

54

52

FastSlow

HighLow

58

56

54

52

Mould Temperature Inject ion Speed

Back Pressure

Main Effects Plot (data means) for Dimension

Interaction Plots


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Mould Temperature

FastS low HighLow

60

55

50

Injection Speed

60

55

50

Back Pr essure

Mould

Temperature

Low

High

Injection

Speed

Slow

Fast

Interaction Plot (data means) for Dimension

Workshop


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Working in teams, conduct a full factorial experiment

(3 factors at 2 levels) using the catapult

Use Minitab to set up the experiment and to analysethe results

Generate at least 4 data points (repeats) at each of the

eight experimental combinations, and use the averagedistance when analysing the results

Remember to Randomise the 8 runs

Analyse your results and prepare a presentation

detailing your findings

Full Factorial - Summary


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Full Factorial experiments have been discussed in thissection because they form the basis for other modes of

experimentation

Full Factorial experiments are not generally used during

the Analyse Phase of the DMAIC because they would

generally require too many runs to complete

In the Analyse Phase, we normally conduct a fraction of

the full factorial (fractional factorial)

A common term for a fractional factorial experiment

carried out in the Analyse Phase is a Screening

Experiment

13 Ssgb Amity Bsi Doe

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