Post on 26-Mar-2015
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: ron@kpa.co.il
Course Website: www.kpa.co.il/biostatCourse textbook: MODERN INDUSTRIAL STATISTICS,
Kenett and Zacks, Duxbury Press, 1998
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
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...
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?
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
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
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
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
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!
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
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
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
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
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
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
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
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
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:
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?
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
?
?
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”
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?
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? ?
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Apr 10, 2023
(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%
Apr 10, 2023
(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
Apr 10, 2023
(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)
Apr 10, 2023
(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
Apr 10, 2023
(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
Apr 10, 2023
(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
Apr 10, 2023
(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
Apr 10, 2023
(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
Apr 10, 2023
(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])
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
Apr 10, 2023
(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
Apr 10, 2023
(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
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
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
Apr 10, 2023
(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
Apr 10, 2023
(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
Apr 10, 2023
(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
Apr 10, 2023
(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
Apr 10, 2023
(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
Apr 10, 2023
(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
Apr 10, 2023
(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