This document provides an overview of design of experiments (DOE). It discusses key concepts like factors, responses, experimental design, and the four basic steps of DOE: plan, collect, analyze, and present. Examples are given to illustrate different types of experimental designs like full factorial designs, fractional factorial designs, and split lot designs. The document also discusses how to identify important factors, characterize relationships, and optimize responses through experimentation.

1. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 1
Design of Experiments
Instructor: Ron S. Kenett
Email: ron@kpa.co.il
Course Website: www.kpa.co.il/biostat
Course textbook: MODERN INDUSTRIAL STATISTICS,
Kenett and Zacks, Duxbury Press, 1998

2. 2-Jun-23
(c) 2001, Ron S. Kenett, 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

3. 2-Jun-23
(c) 2001, Ron S. Kenett, 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...

4. 2-Jun-23
(c) 2001, Ron S. Kenett, 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?

5. 2-Jun-23
(c) 2001, Ron S. Kenett, 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
Film
Building
Chemical
Process
Digital
Imaging

6. 2-Jun-23
(c) 2001, Ron S. Kenett, 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

7. 2-Jun-23
(c) 2001, Ron S. Kenett, 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

8. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 8
Cycle of Experimentation
COLLECT
Observe
Code
PLAN
Questions
Design
Scope
PRESENT
Answer Questions
Graphically
Mathematically
State Uncertainty
Recommend
ANALYZE
Plot
Plot
Plot
Model
Conclude
Four Basic Steps of DOE

9. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 9
A Serious Problem...
I want my
car to go
fast … like
that one!

10. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 10
What Factors Affect the Speed?
Key Factor is: ___________________
Yes
Air Holes
No
Slow
Fast
Shape

11. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 11
Key Factor is: _______________________________
Yes
Air Holes
No
Slow
Fast
Slow
Shape
Effect of Air Holes

12. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 12
DOE Balanced Effects
Key Factor is: _______________________________
Yes
Air Holes
No
Slow
Fast
Slow
Shape
Slow

13. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 13
What factors affect
flight time?
What factors affect the
quality of flight?
The Helicopter Company

14. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 14
Length
Width
Factors
Design Wing Wing
Length Width
1 2.5 1.0
2 3.5 1.0
3 2.5 1.5
4 3.5 1.5
Response: Flight Time
Your Experiment: Plan

15. 2-Jun-23
(c) 2001, Ron S. Kenett, 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

16. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 16
Calculate averages for each design
Wing Width
1.0 1.5
(1)
(2)
(3)
(4)
2.5
3.5
Wing
Length
Avg. ___ Avg. ___
Avg. ___
Avg. ___
Your Experiment: Analyze

17. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 17
Your Experiment: Analyze
Plot the data (one line for each Wing Width)
Time
2.5
Wing Length
3.5

18. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 18
Your Experiment: Present
Present
 Answer the original question:
Which factor most affects flight time?
 Graphically
 Numerically
Recommendations:

19. 2-Jun-23
(c) 2001, Ron S. Kenett, 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?

20. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 20
Health Imaging Customer Preference Study
• Conventional thinking:
Low noise a
customer requirement
• Some data suggested that
high resolution (MTF) was
larger driver
• Experiment designed to
identify key driver
Which Is the Key Driver?
MTF
Hi
Low
Low Hi
Noise
1
4
?
?

21. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 21
X2
X1
“Homerun”
X2
X1
“Shotgun”
X2
X1
“Factorial”
How Many Experiments?
X2
X1
“1-at-a-
time”

22. 2-Jun-23
(c) 2001, Ron S. Kenett, 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?
Fractional
Factorial?
Linear
Response?
Curvature?

23. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 23
A A A A A B B B B B
A B
Is B better than A ?

24. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 24
-
-
-
Split Lot Design
A
B
A
B
A
B
A
B
A
B
A
B

25. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 25
Factors and Levels
Factors
 Paste
 Dielectric
 Oven
Levels
-1 +1
-1 +1
-1 +1

26. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 26
Paste DielectOven Response
-1 -1 -1 119
1 -1 -1 44
-1 1 -1 232
1 1 -1 135
-1 -1 1 11
1 -1 1 34
-1 1 1 45
1 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

27. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 27
Oven
Dielect
Paste
1
-1
1
-1
1
-1
130
110
90
70
50
Response
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 Plot

28. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 28
1
-1
1
-1
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 Plots

29. 2-Jun-23
(c) 2001, Ron S. Kenett, 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

30. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 30
0.6460
0.6500
0.6570
0.6540
0.6590
0.6570
0.6620
0.6580
1.2470
1.2350
1.2760
1.2480
1.3010
1.2880
1.2990
1.2840
0.1920
0.2150
0.2060
0.1880
0.2210
0.1990
0.1930
0.1920
0.3360
0.3850
0.3320
0.3220
0.3780
0.3550
0.3630
0.3530
0.6810
0.6780
0.6810
0.6820
0.6810
0.6820
0.6830
0.6800
1.4680
1.4590
1.4680
1.4790
1.4920
1.4720
1.4810
1.5040
0.4600
0.4690
0.4400
0.4250
0.4350
0.4120
0.4120
0.4460
0.9030
0.8280
0.9640
0.8360
0.8670
0.9380
0.9450
0.9730
0.4640
0.4610
0.4640
0.4600
0.4660
0.4670
0.4660
0.4650
0.9110
0.8950
0.8960
0.8970
0.9300
0.9220
0.9060
0.9260
0.1390
0.1310
0.1330
0.1480
0.1490
0.1690
0.1440
0.1490
0.2370
0.2340
0.2380
0.2400
0.2470
0.2260
0.2220
0.2720
0.4820
0.4810
0.4810
0.4810
0.4830
0.4820
0.4810
0.4830
1.0340
1.0360
1.0400
1.0270
1.0450
1.0570
1.0510
1.0370
0.3390
0.3200
0.3290
0.3170
0.2790
0.3180
0.3300
0.3200
0.6930
0.5790
0.6560
0.6780
0.6390
0.5880
0.6570
0.6500
G
F
E
D
C
B
A
1
-1
1
-1
1
-1
1
-1
1
-1
1
-1
1
-1
Cube Plot - Means for Average
27 Full Factorial Design

31. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 31
G
F
E
D
C
B
A
0.8
0.7
0.6
0.5
0.4
Average 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
1
-1
1
-1
1
-1
1
-1
1
-1
1
-1
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

32. 2-Jun-23
(c) 2001, Ron S. Kenett, 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
.999
P
robability
Eff_Avg
Average: 0.0198583
Std Dev: 0.203497
N of data: 15
Anderson-Darling Normality Test
A-Squared: 0.480
p-value: 0.199
Normal Probability Plot
C_I niV ol
A _Weight
D_Spring
B _Surfac
CD
27 Full Factorial Design

33. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 33
Size of Full Factorial Designs

34. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 34
A B C AB AC BC ABC
-
-
+
+
Fractional Factorial Design

35. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 35
135
34
45
119
Oven
Dielect
Paste
1
-1
1
-1
1
-1
Cube Plot - Means for Response
Paste DielectOven Response
-1 -1 -1 119
1 -1 -1 44
-1 1 -1 232
1 1 -1 135
-1 -1 1 11
1 -1 1 34
-1 1 1 45
1 1 1 80
23-1 Fractional Factorial Design

36. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 36
A B C D E F G
0.5
0.6
0.7
0.8
0.9
Average
M
ain Effects Plot - M
eans for Average
2 ^(7 -3 ) = 1
6
16
A B C D E F G
0.5
0.6
0.7
0.8
0.9
Average
M
ain Effects Plot - M
eans for Average
2^(7-2 ) = 3 2
32
A B C D E F G
0.40
0.52
0.64
0.76
0.88
Average
M
ain Effects Plot - M
eans for Average
2 ^(7 -1
) = 6 4
64

37. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 37
B_Surf C_IniVol D_Spring G_GasTem Average Std_Dev
-1 -1 -1 -1 0.789 0.2104
1 -1 -1 -1 0.536 0.2691
-1 1 -1 -1 0.925 0.0174
1 1 -1 -1 0.504 0.2455
-1 -1 1 -1 0.486 0.1130
1 -1 1 -1 0.407 0.1667
-1 1 1 -1 0.528 0.1121
1 1 1 -1 0.446 0.1580
-1 -1 -1 1 0.420 0.1194
1 -1 -1 1 0.649 0.2503
-1 1 -1 1 0.520 0.2325
1 1 -1 1 0.335 0.0577
-1 -1 1 1 0.492 0.1366
1 -1 1 1 0.458 0.1186
-1 1 1 1 0.456 0.1464
1 1 1 1 0.424 0.1279
2 0 0 0 0.659 0.1476
-2 0 0 0 0.546 0.1945
0 2 0 0 0.602 0.1538
0 -2 0 0 0.517 0.1674
0 0 2 0 0.293 0.0874
0 0 -2 0 0.611 0.4334
0 0 0 2 0.422 0.2229
0 0 0 -2 0.623 0.2401
0 0 0 0 0.412 0.1285
0 0 0 0 0.456 0.1377
0 0 0 0 0.376 0.1105
0 0 0 0 0.483 0.2034
Central
Composite
Designs

38. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 38
0.3
-2
0.4
0.5
-2
0.6
-1
0.7
0.8
-1
0.9
0
1.0
0
1
1
2 2
0.4
-2
0.5
0.6
-2
-1
0.7
-1
0.8
0
0.9
0
1
1
2 2
Response Surfaces of Piston Performance
0.3
-2
0.4
-2
0.5
-1
0.6
-1
0
0.7
0
1
1
2 2
0.35
-2
0.45
0.55
0.65
-2
-1
0.75
0.85
-1
0.95
0
1.05
0
1
1
2 2
0.3
-2
0.4
0.5
-2
-1
0.6
0.7
-1
0.8
0
0.9
0
1
1
2 2
0.4
-2
0.5
0.6
-2
-1
0.7
0.8
-1
0
0.9
0
1
1
2 2

39. 2-Jun-23
(c) 2001, Ron S. Kenett, 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 m
Cubicity >60%
 Goal: What is the operating window for getting
the desired grain size and cubicity?
A
Case Study

40. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 40
Experimental Design
3 x 3 factorial design
30
18
6
0.388
69%
0.634
65%
0.754
60%
0.987
61%
0.821
47%
0.655
80%
1.259
48%
Flow
(cc/min)
13.2 39.6 66
Ripener (cc) A
Case Study
0.543
76%
0.967
46%

41. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 41
0.50
0.60
0.70
0.80
0.86
0.90
1.00
1.10
1.20
Size
Mapping the Effects: Grain Size
FLOW
(cc/min)
RIPENER (cc)
A
Case Study

42. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 42
Cubicity
77%
72%
67%
62%
57%
52%
47%
Mapping the Effects: Cubicity
FLOW
(cc/min)
A
Case Study
RIPENER (cc)

43. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 43
Where Is the Overlap?
FLOW
(cc’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
A
Case Study

44. 2-Jun-23
(c) 2001, Ron S. Kenett, 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 branded
photofinishing option be priced?
What share of choice can we expect?
B
Case Study

45. 2-Jun-23
(c) 2001, Ron S. Kenett, 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
B
Case Study

46. 2-Jun-23
(c) 2001, Ron S. Kenett, 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
B
Case 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

47. 2-Jun-23
(c) 2001, Ron S. Kenett, 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)
B
Case Study

48. 2-Jun-23
(c) 2001, Ron S. Kenett, 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 $10.29
Price of KPP
Next Day KPP Same Day
B
Case Study
Cell 1 - Mass Merchant
(Same Day =$6.99 [median] and Next Day = $3.99 [median])

49. 2-Jun-23
(c) 2001, Ron S. Kenett, 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
B
Case Study

50. 2-Jun-23
(c) 2001, Ron S. Kenett, 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
B
Case Study

51. 2-Jun-23
(c) 2001, Ron S. Kenett, 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
B
Case Study

52. 2-Jun-23
(c) 2001, Ron S. Kenett, 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%
B
Case Study

53. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 53
a 25-1 Fractional Factorial Experiment
1. Purity by SE-HPLC
2. O.D.
 Responses

54. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 54
 Factors
A. Freeze Temperature
B. Thaw Temperature
C. Volume
D. Concentration
E. Bulk

55. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 55
 Levels
FACTOR Low High
A:FreezeTemp-196 -70
B:ThawRemp 5 23
C:Volume 1.8 200
D:Concprot 0.35 0.5
E:Bulk a b

56. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 56
 Choosing the Experimental Array - 1
Fractional Factorial Design
Factors: 5 Base Design: 5, 16
Runs: 32 Replicates: 2
Blocks: none Center p
Design Generators: E = ABCD

57. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 57
 Choosing the Experimental Array - 2
Design Generators: E = ABCD
Alias Structure
I + ABCDE
A + BCDE, B + ACDE, C + ABDE, D + ABCE, E
+ ABCD
AB + CDE, AC + BDE, AD + BCE, AE + BCD,
BC + ADE
BD + ACE, BE + ACD, CD + ABE, CE + ABD,
DE + ABC

58. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 58
FreezeTemp ThawTemp Volume Concprot Bulk
-196 5 1.8 0.35 b
-70 5 1.8 0.35 a
-196 23 1.8 0.35 a
-70 23 1.8 0.35 b
-196 5 200.0 0.35 a
-70 5 200.0 0.35 b
-196 23 200.0 0.35 b
-70 23 200.0 0.35 a
-196 5 1.8 0.50 a
-70 5 1.8 0.50 b
-196 23 1.8 0.50 b
-70 23 1.8 0.50 a
-196 5 200.0 0.50 b
-70 5 200.0 0.50 a
-196 23 200.0 0.50 a
-70 23 200.0 0.50 b

59. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 59
-196 -70
0.35 0.50
FreezeTemp
ThawTemp
Volume
Concprot
Bulk
5
23
b
a
1.8
200.0
2^(5-1) Fractional Factorial Design

60. 2-Jun-23
(c) 2001, Ron S. Kenett, Ph.D. 60
 Protocol of Experiment
Two Independent samples for each run
Each sample will be tested in duplicate
a) Take the two bulks
b) Dilute the two bulks at 0.5 and 0.35 mg/ml
c) Take all the samples at the two freezing temperature conditions
d) Take all the samples at the two thawing temperature conditions
e) Start the analysis