2-jan-14 (c) 2001, ron s. kenett, ph.d.1 design of experiments instructor: ron s. kenett email:...

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Jun 22, 2022 (c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D. Ph.D. 1 Design of Experiments Instructor: Ron S. Kenett Email: [email protected] Course Website: www.kpa.co.il/biostat Course textbook: MODERN INDUSTRIAL STATISTICS, Kenett and Zacks, Duxbury Press, 1998

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Page 1: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 1

Design of Experiments

Instructor: Ron S. KenettEmail: [email protected]

Course Website: www.kpa.co.il/biostatCourse textbook: MODERN INDUSTRIAL STATISTICS,

Kenett and Zacks, Duxbury Press, 1998

Page 2: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 2

Course Syllabus

•Understanding Variability•Variability in Several Dimensions•Basic Models of Probability•Sampling for Estimation of Population Quantities•Parametric Statistical Inference•Computer Intensive Techniques•Multiple Linear Regression•Statistical Process Control•Design of Experiments

Page 3: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 3

DOE Is a Problem-Solving Tool

The color is too saturated...

When you have a serious problem...

… you need a good problem solving tool!

We get banding when...

The order wasn’t delivered

on time...

Page 4: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 4

• Which factors have the strongest effects?• Do any of the factors interact?• Which factor settings give the best results?

DOE Helps Answer Key Questions

The media jams when we

print...

Lubricant?

Exit angle?

Spring tension?

Page 5: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 5

Process, Responses, and Factors -1

Factors

Silver laydown, Finish time…

Time,Catalyst…

Transport speed,Capture lens...

Responses

Speed,Contrast

Yield,Purity

Image resolution,Banding

FilmBuilding

ChemicalProcess

Digital Imaging

Page 6: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 6

Factors

Compensation plan, Sales training

Method of shipping, Order entry method

Product positioning,Price

Responses

Sales revenue, Volume of new sales

Shipping cost, Inventory level

Trial purchase,Share of market

Sales

Supply Chain

Product Develop.

Process, Responses, and Factors -2

Page 7: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 7

Screen: Which are the biggest factors?

Characterize: What is the relationship between responses and factors?

Optimize: What is the best setting of the factors?

Verify: Are the results repeatable?

Ask a Series of Questions

Question Experiment(E) Q E Q E Q E (Q)

Answer A A A

Page 8: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 8

Cycle of Experimentation

COLLECTObserveCode

PLANQuestionsDesignScope

PRESENTAnswer QuestionsGraphicallyMathematicallyState UncertaintyRecommend

ANALYZEPlotPlotPlotModelConclude

Four Basic Steps of DOE

Page 9: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 9

A Serious Problem...

I want my car to go

fast … like that one!

Page 10: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 10

What Factors Affect the Speed?

Key Factor is: ___________________

Yes

Air Holes

No

Slow

Fast

Shape

Page 11: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 11

Key Factor is: _______________________________

Yes

Air Holes

No

Slow

FastSlow

Shape

Effect of Air Holes

Page 12: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 12

DOE Balanced Effects

Key Factor is: _______________________________

Yes

Air Holes

No

Slow

FastSlow

Shape

Slow

Page 13: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 13

What factors affect flight time?

What factors affect the quality of flight?

The Helicopter Company

Page 14: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 14

Length

Width

Factors

Design Wing WingLength Width

1 2.5 1.02 3.5 1.03 2.5 1.54 3.5 1.5

Response: Flight Time

Your Experiment: Plan

Page 15: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 15

Design # Repeat Test Wing Wing Flight Quality Flight Order Length Width Time of Flight

1

1

2

2

3

3

4

4

1

2

1

2

1

2

1

2

2.5

2.5

3.5

3.5

2.5

2.5

3.5

3.5

1.0

1.0

1.0

1.0

1.5

1.5

1.5

1.5

Your Experiment: Collect

Page 16: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 16

Calculate averages for each design

Wing Width

1.0 1.5

(1)

(2)

(3)

(4)

2.5

3.5

WingLength

Avg. ___ Avg. ___

Avg. ___

Avg. ___

Your Experiment: Analyze

Page 17: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 17

Your Experiment: Analyze

Plot the data (one line for each Wing Width)

Time

2.5Wing Length

3.5

Page 18: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 18

Your Experiment: Present

Present Answer the original question:

Which factor most affects flight time?

Graphically Numerically

Recommendations:

Page 19: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 19

What about Quality of Flight?

Is quality of flight related to flight time, or rotational speed, a combination, or something else entirely?

Does everyone think about this response in the same way?

What are the implications for analysis?

Page 20: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 20

Health Imaging Customer Preference Study

• Conventional thinking: Low noise a customer requirement

• Some data suggested thathigh resolution (MTF) was larger driver

• Experiment designed to identify key driver

Which Is the Key Driver?

MTF

Hi

Low

Low Hi

Noise

1

4

?

?

Page 21: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 21

X2

X1

“Homerun”

X2

X1

“Shotgun”

X2

X1

“Factorial”

How Many Experiments ?

X2

X1

“1-at-a-time”

Page 22: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 22

?Typical Questions

Full factorial experiments can require many runs

The problem is greater if the response is nonlinear

Talk with an expert to decide how the experiment should be structured

Full Factorial?

FractionalFactorial?

Linear Response?

Curvature?

Page 23: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 23

A A A A A B B B B BA B

0

5

10

15

20

25

30

35

40

1 2 3 4 5 6 7 8 9 10 11 12

Is B better than AIs B better than A? ?

Page 24: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 24

-3

-2

-1

0

1

2

3

4

5

1 2 3 4 5 6 7 8 9 10 11 12

Split Lot DesignSplit Lot Design

A

B

A

B

A

B

A

B

A

B

A

B

Page 25: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 25

Factors and Levels

Factors Paste Dielectric Oven

Levels-1 +1-1 +1-1 +1

Page 26: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 26

Paste DielectOven Response-1 -1 -1 1191 -1 -1 44-1 1 -1 2321 1 -1 135-1 -1 1 111 -1 1 34-1 1 1 451 1 1 80

44

34

135

80

119

11

232

45

-1 1

Paste

Dielect

Oven-1

1

-1

1

Cube Plot - Means for Response

23 Full Factorial Design

44

34

135

80

119

11

232

45

-1 1

Paste

Dielect

Oven-1

1

-1

1

Cube Plot - Means for Response

Page 27: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 27

OvenDielectPaste

130

110

90

70

50

Res

pons

e

Main Effects for Response

44

34

135

80

119

11

232

45

-1 1

Paste

Dielect

Oven-1

1

-1

1

Cube Plot - Means for Response

Main Effects PlotMain Effects Plot

Page 28: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 28

Oven

Dielect

Paste

1

-1

1

-1

Interaction Plot for Response

44

34

135

80

119

11

232

45

-1 1

Paste

Dielect

Oven-1

1

-1

1

Cube Plot - Means for Response

Interaction PlotsInteraction Plots

Page 29: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 29

C: Initial Gas Volume (m3)

B: Piston Surface Area (m2)A: Piston Weight (Kg)

D: Spring Coefficient (N/m)

E: Atmospheric Pressure (N/m2)F: Ambient Temperature (0K)

G: Gas Temperature (0K)

27 Full Factorial Design

Page 30: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 30

0.64600.6500

0.65700.6540

0.65900.6570

0.66200.6580

1.24701.2350

1.27601.2480

1.30101.2880

1.29901.2840

0.19200.2150

0.20600.1880

0.22100.1990

0.19300.1920

0.33600.3850

0.33200.3220

0.37800.3550

0.36300.3530

0.68100.6780

0.68100.6820

0.68100.6820

0.68300.6800

1.46801.4590

1.46801.4790

1.49201.4720

1.48101.5040

0.46000.4690

0.44000.4250

0.43500.4120

0.41200.4460

0.90300.8280

0.96400.8360

0.86700.9380

0.94500.9730

0.46400.4610

0.46400.4600

0.46600.4670

0.46600.4650

0.91100.8950

0.89600.8970

0.93000.9220

0.90600.9260

0.13900.1310

0.13300.1480

0.14900.1690

0.14400.1490

0.23700.2340

0.23800.2400

0.24700.2260

0.22200.2720

0.48200.4810

0.48100.4810

0.48300.4820

0.48100.4830

1.03401.0360

1.04001.0270

1.04501.0570

1.05101.0370

0.33900.3200

0.32900.3170

0.27900.3180

0.33000.3200

0.69300.5790

0.65600.6780

0.63900.5880

0.65700.6500

G

F

E

D

CB

A

1-1 1-1

1-1

1

-1

1

-1

1

-1 1

-1

Cube Plot - Means for Average

27 Full Factorial Design

Page 31: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 31

GFEDCBA

0.8

0.7

0.6

0.5

0.4

Ave

rage

Main Effects Plot - Means for Average

A: Piston Weight

(Kg)

B: Piston Surface Area

(m2)

C: Initial Gas

Volume (m3)

D: Spring Coefficient

(N/m)

E: Atmospheric

Pressure (N/m2)

F: Ambient Temperature

(0K)

G: Gas Temperature

(0K)

128

G

F

E

D

C

B

A

1-1

1-1

1-1

1-1

1-1

1-1

Interaction Plot for Average

27 Full Factorial Design

Page 32: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 32

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5

.001

.01

.05

.20

.50

.80

.95

.99

.999Pr

obab

ility

Eff_AvgAverage: 0.0198583Std Dev: 0.203497N of data: 15

Anderson-Darling Normality TestA-Squared: 0.480p-value: 0.199

Normal Probability Plot

C_IniVolA_Weight

D_Spring

B_Surfac

CD

27 Full Factorial Design

Page 33: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 33

6 647 1288 2569 512

10 102411 204812 409613 819214 1638415 32768

Size of Full Factorial Designs

Page 34: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 34

-1 -1 -1 1 1 1 -11 -1 -1 -1 -1 1 1

-1 1 -1 -1 1 -1 11 1 -1 1 -1 -1 -1

-1 -1 1 1 -1 -1 11 -1 1 -1 1 -1 -1

-1 1 1 -1 -1 1 -11 1 1 1 1 1 1

-1 -1 -1 1 1 1 -11 -1 -1 -1 -1 1 1

-1 1 -1 -1 1 -1 11 1 -1 1 -1 -1 -1

-1 -1 1 1 -1 -1 11 -1 1 -1 1 -1 -1

-1 1 1 -1 -1 1 -11 1 1 1 1 1 1

A B C AB AC BC ABCA B C AB AC BC ABC

-

-

+

+

Fractional Factorial Design

Page 35: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 35

135

34

45

119Oven

Dielect

Paste 1-1

1

-1

1

-1

Cube Plot - Means for Response

Paste DielectOven Response-1 -1 -1 1191191 -1 -1 44-1 1 -1 2321 1 -1 135135-1 -1 1 111 -1 1 3434-1 1 1 45451 1 1 80

23-1 Fractional Factorial Design

Page 36: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 36

A B C D E F G

0.5

0.6

0.7

0.8

0.9

Average

Main Effects Plot - Means for Average

2 (̂7-3) = 16

A B C D E F G

0.5

0.6

0.7

0.8

0.9

Average

Main Effects Plot - Means for Average

2 (̂7-3) = 16

1616

A B C D E F G

0.5

0.6

0.7

0.8

0.9

Average

Main Effects Plot - Means for Average

2 (̂7-2) = 32

A B C D E F G

0.5

0.6

0.7

0.8

0.9

Average

Main Effects Plot - Means for Average

2 (̂7-2) = 3232

A B C D E F G

0.40

0.52

0.64

0.76

0.88

Average

Main Effects Plot - Means for Average

2 (̂7-1) = 64

A B C D E F G

0.40

0.52

0.64

0.76

0.88

Average

Main Effects Plot - Means for Average

2 (̂7-1) = 64

64

Page 37: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 37

B_SurfB_Surf C_IniVolC_IniVol D_SpringD_Spring G_GasTemG_GasTem AverageAverage Std_DevStd_Dev-1 -1 -1 -1 0.789 0.21041 -1 -1 -1 0.536 0.2691-1 1 -1 -1 0.925 0.01741 1 -1 -1 0.504 0.2455-1 -1 1 -1 0.486 0.11301 -1 1 -1 0.407 0.1667-1 1 1 -1 0.528 0.11211 1 1 -1 0.446 0.1580-1 -1 -1 1 0.420 0.11941 -1 -1 1 0.649 0.2503-1 1 -1 1 0.520 0.23251 1 -1 1 0.335 0.0577-1 -1 1 1 0.492 0.13661 -1 1 1 0.458 0.1186-1 1 1 1 0.456 0.14641 1 1 1 0.424 0.12792 0 0 0 0.659 0.1476-2 0 0 0 0.546 0.19450 2 0 0 0.602 0.15380 -2 0 0 0.517 0.16740 0 2 0 0.293 0.08740 0 -2 0 0.611 0.43340 0 0 2 0.422 0.22290 0 0 -2 0.623 0.24010 0 0 0 0.412 0.12850 0 0 0 0.456 0.13770 0 0 0 0.376 0.11050 0 0 0 0.483 0.2034

CentralComposite

Designs

Page 38: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 38

0.3-2

0.40.5

-2

0.6

-1

0.7

0.8

-1

0.9

0

1.0

01

12 2

0.4

-2

0.5

0.6

-2-1

0.7

-1

0.8

0

0.9

01

12 2

Response Surfaces of Piston Performance

0.3-2

0.4

-2

0.5

-1

0.6

-10

0.7

01

12 2

0.35-2

0.45

0.55

0.65

-2-1

0.75

0.85

-1

0.95

0

1.05

01

12 2

0.3-2

0.4

0.5

-2-1

0.6

0.7

-1

0.8

0

0.9

01

12 2

0.4-2

0.5

0.6

-2-1

0.7

0.8

-10

0.9

01

12 2

Page 39: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 39

Case Study A: Manufacturing

Health Imaging Development Program New mammography film

(Kodak Min R-2000 film) Emulsion making (cubes)

Factors: Ripener level, nucleation flow rate Aims: Grain size 0.80 - 0.86

Cubicity >60% Goal: What is the operating window for getting

the desired grain size and cubicity?

ACase Study

Page 40: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

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(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 40

Experimental Design

3 x 3 factorial design

30

18

6

0.38869%

0.63465%

0.754 60%

0.98761%

0.82147%

0.65580%

1.25948%

Flow(cc/min)

13.2 39.6 66

Ripener (cc) ACase Study

0.54376%

0.96746%

Page 41: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

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(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 41

0.500.60

0.70

0.800.86

0.90

1.00

1.10

1.20

Size

Mapping the Effects: Grain Size

FL

OW

(c

c/m

in)

RIPENER (cc)

ACase Study

Page 42: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

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(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 42

Cubicity

77%

72%

67%

62%

57%

52%

47%

Mapping the Effects: Cubicity

FL

OW

(c

c/m

in)

ACase StudyRIPENER (cc)

Page 43: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

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(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 43

Where Is the Overlap?

FL

OW

(c

c’s

/min

)

RIPENER (cc’s)

77%

72%

67%62%

57%

52%

47%

0.50 0.60 0.70

0.80

0.86 0.90

1.00

1.10

1.20

ACase Study

Page 44: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

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(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 44

Case Study B: Business Units

Consumer Imaging New opportunity for branded photofinishing

in the United States Differentiation, pricing, segmentation all

important considerations

Question: How should a Kodak brandedphotofinishing option be priced?

What share of choice can we expect?

BCase Study

Page 45: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

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(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 45

Methodology

Mall intercept interviews with 100 consumers per cell who:

Have used at least three rolls of 35 mm film in the past year, and

Are responsible for deciding on photofinishing

Respondents complete “choice” exercises that simulate purchase decisions

BCase Study

Page 46: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

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(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 46

CELL 1:

Price Levels for Mass Merchant

Store Processing:

Overnight $3.49 $3.99 $4.99

Same Day $6.24 $6.99 $7.49

KODAK Premium Processing Bundle:

Photofile $8.29 $9.29 $10.29

Price Levels

BCase Study

CELL 2:

Price Levels for Drug/Food

Store Processing:

Overnight $4.49 $4.99 $5.99

Same Day $6.99 $7.99 $8.49

KODAK Premium Processing Bundle:

Photofile $8.29 $9.29 $10.29

Page 47: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

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(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 47

Choice Example

9 cards per person

In-Store Overnight Processing

$3.99

In-Store Same Day Processing

$6.99

KODAK Premium

Processing

$9.29

Choice cards in study simulated Point of Sale (POS)

BCase Study

Page 48: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

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(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 48

Results: Mass Merchant

57%63%63%

34%23%26%

10% 10% 14%0%

20%

40%

60%

80%

100%

$8.29 $9.29 $10.29Price of KPP

Next Day KPP Same Day

BCase Study

Cell 1 - Mass Merchant(Same Day =$6.99 [median] and Next Day = $3.99 [median])

Page 49: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 49

Cell 2 - Drug/Food(Same Day =$7.99 [median] and Next Day = $4.99 [median])

Results: Drug/Food

58%67%

60%

35%22%26%

7%14% 11%0%

20%

40%

60%

80%

100%

$8.29 $9.29 $10.29

Price of KODAK Premium Processing Next Day KODAK Premium Processing Same Day

BCase Study

Page 50: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

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(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 50

Cell 1 - Mass Merchant(Same Day =$6.24 [low] and Next Day = $3.49 [low])

Results: Mass Merchant

58%63%64%

29%19%22%

13% 14% 18%0%

20%

40%

60%

80%

100%

$8.29 $9.29 $10.29

Price of KODAK Premium Processing Next Day KODAK Premium Processing Same Day

BCase Study

Page 51: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

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(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 51

Cell 2 - Drug/Food(Same Day =$6.99 [low] and Next Day = $4.49 [low])

Results: Drug/Food

61%69%

62%

31%19%22%

8%16% 13%

0%

20%

40%

60%

80%

100%

$8.29 $9.29 $10.29

Price of KODAK Premium Processing Next Day KODAK Premium Processing Same Day

BCase Study

Page 52: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 52

Model: Share of Choice Calculator

INPUTS:

Market: Mass Merchant

Price for Same Day Processing: $6.99

Price for Next Day Processing: $3.99

Price for KODAK Premium Processing : $9.29

MODEL ESTIMATES:

Share of Choice for KODAK Premium Processing : 26%

Share of Choice for Same Day: 10%Share of Choice for Next Day: 63% BCase Study

Page 53: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

Apr 10, 2023

(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 53

a 25-1 Fractional Factorial Experiment

1. 1. Purity by SE-HPLCPurity by SE-HPLC2. 2. O.D.O.D.

Responses

Page 54: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

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(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 54

Factors

A. A. Freeze TemperatureFreeze TemperatureB. B. Thaw TemperatureThaw TemperatureC. C. VolumeVolumeD. D. ConcentrationConcentrationE. E. BulkBulk

Page 55: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

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(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 55

LevelsFACTORFACTOR LowLow HighHighA:FreezeTempA:FreezeTemp-196-196 -70-70B:ThawRempB:ThawRemp 55 2323C:VolumeC:Volume 1.81.8 200200D:ConcprotD:Concprot 0.350.35 0.50.5E:BulkE:Bulk aa bb

Page 56: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

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(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 56

Choosing the Experimental Array - 1

Fractional Factorial DesignFractional Factorial Design

Factors: 5 Base Design: 5, 16 Resolution: VFactors: 5 Base Design: 5, 16 Resolution: VRuns: 32 Replicates: 2 Runs: 32 Replicates: 2 Fraction: 1/2 Fraction: 1/2

Blocks: none Center pts (total): 0Blocks: none Center pts (total): 0

Design Generators: E = ABCD Design Generators: E = ABCD

Page 57: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

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(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 57

Choosing the Experimental Array - 2

Design Generators: E = ABCDDesign Generators: E = ABCD

Alias StructureAlias Structure

I + ABCDEI + ABCDE

A + BCDE, B + ACDE, C + ABDE, D + ABCE, E A + BCDE, B + ACDE, C + ABDE, D + ABCE, E + ABCD+ ABCDAB + CDE, AC + BDE, AD + BCE, AE + BCD, AB + CDE, AC + BDE, AD + BCE, AE + BCD, BC + ADEBC + ADEBD + ACE, BE + ACD, CD + ABE, CE + ABD, BD + ACE, BE + ACD, CD + ABE, CE + ABD, DE + ABCDE + ABC

Page 58: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

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(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 58

FreezeTempFreezeTemp ThawTempThawTemp VolumeVolume ConcprotConcprot BulkBulk-196-196 55 1.81.8 0.350.35 bb-70-70 55 1.81.8 0.350.35 aa-196-196 2323 1.81.8 0.350.35 aa-70-70 2323 1.81.8 0.350.35 bb-196-196 55 200.0200.0 0.350.35 aa-70-70 55 200.0200.0 0.350.35 bb-196-196 2323 200.0200.0 0.350.35 bb-70-70 2323 200.0200.0 0.350.35 aa-196-196 55 1.81.8 0.500.50 aa-70-70 55 1.81.8 0.500.50 bb-196-196 2323 1.81.8 0.500.50 bb-70-70 2323 1.81.8 0.500.50 aa-196-196 55 200.0200.0 0.500.50 bb-70-70 55 200.0200.0 0.500.50 aa-196-196 2323 200.0200.0 0.500.50 aa-70-70 2323 200.0200.0 0.500.50 bb

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(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 59

-196 -700.35 0.50FreezeTemp

ThawTempVolume

Concprot

Bulk

5

23

b

a

1.8

200.0

2^(5-1) Fractional Factorial Design

Page 60: 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website:

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(c) 2001, Ron S. Kenett, (c) 2001, Ron S. Kenett, Ph.D.Ph.D. 60

Protocol of Experiment

Two Independent samples for each runTwo Independent samples for each runEach sample will be tested in duplicateEach sample will be tested in duplicate

a) Take the two bulksa) Take the two bulksb) Dilute the two bulks at 0.5 and 0.35 mg/mlb) Dilute the two bulks at 0.5 and 0.35 mg/mlc) Take all the samples at the two freezing temperature conditionsc) Take all the samples at the two freezing temperature conditionsd) Take all the samples at the two thawing temperature conditionsd) Take all the samples at the two thawing temperature conditionse) Start the analysise) Start the analysis