Sas DESIGN OF EXPERIMENTS RELEASE 9 User Manual
Design of Experiments
Guide
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Release 9
Design of Experiments
Guide
“The real voyage of discovery consists not in seeking new
landscapes, but in having new eyes.”
Marcel Proust
JMP, A Business Unit of SAS
SAS Campus Drive
Cary, NC 27513
The correct bibliographic citation for this manual is as follows: SAS Institute Inc. 2009. JMP® 9 Design
of Experiments Guide, Second Edition. Cary, NC: SAS Institute Inc.
®
JMP
9 Design of Experiments Guide, Second Edition
Copyright © 2010, SAS Institute Inc., Cary, NC, USA
ISBN 978-1-60764-597-9
All rights reserved. Produced in the United States of America.
For a hard-copy book: No part of this publication may be reproduced, stored in a retrieval system, or
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documentation by the U.S. government is subject to the Agreement with SAS Institute and the
restrictions set forth in FAR 52.227-19, Commercial Computer Software-Restricted Rights (June 1987).
SAS Institute Inc., SAS Campus Drive, Cary, North Carolina 27513.
1st printing, September 2010
®
JMP
, SAS® and all other SAS Institute Inc. product or service names are registered trademarks or
trademarks of SAS Institute Inc. in the USA and other countries. ® indicates USA registration.
Other brand and product names are registered trademarks or trademarks of their respective companies.
1 Introduction to Designing Experiments
A Beginner’s Tutorial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
About Designing Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
My First Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
The Situation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Step 1: Design the Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Step 2: Define Factor Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Step 3: Add Interaction Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Step 4: Determine the Number of Runs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Step 5: Check the Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Step 6: Gather and Enter the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Step 7: Analyze the Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2 Examples Using the Custom Designer
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Creating Screening Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Creating a Main-Effects-Only Screening Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Creating a Screening Design to Fit All Two-Factor Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
A Compromise Design Between Main Effects Only and All Interactions . . . . . . . . . . . . . . . . . . . . 20
Creating ‘Super’ Screening Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Screening Designs with Flexible Block Sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Checking for Curvature Using One Extra Run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Contents
Design of Experiments
Creating Response Surface Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Exploring the Prediction Variance Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Introducing I-Optimal Designs for Response Surface Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
A Three-Factor Response Surface Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Response Surface with a Blocking Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Creating Mixture Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Mixtures Having Nonmixture Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Experiments that are Mixtures of Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
ii
Special-Purpose Uses of the Custom Designer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Designing Experiments with Fixed Covariate Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Creating a Design with Two Hard-to-Change Factors: Split Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Technical Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3 Building Custom Designs
The Basic Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
Creating a Custom Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Enter Responses and Factors into the Custom Designer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Describe the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Specifying Alias Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
Select the Number of Runs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Understanding Design Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Specify Output Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Make the JMP Design Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Creating Random Block Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Creating Split Plot Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Creating Split-Split Plot Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Creating Strip Plot Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Special Custom Design Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
Save Responses and Save Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Load Responses and Load Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Save Constraints and Load Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Set Random Seed: Setting the Number Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Simulate Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Save X Matrix: Viewing the Number of Rows in the Moments Matrix and the Design Matrix (X) in the
Log . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Optimality Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Number of Starts: Changing the Number of Random Starts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Sphere Radius: Constraining a Design to a Hypersphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Disallowed Combinations: Accounting for Factor Level Restrictions . . . . . . . . . . . . . . . . . . . . . . . 90
Advanced Options for the Custom Designer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Save Script to Script Window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Assigning Column Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Define Low and High Values (DOE Coding) for Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Set Columns as Factors for Mixture Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Define Response Column Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Assign Columns a Design Role . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Identify Factor Changes Column Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
How Custom Designs Work: Behind the Scenes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4 Screening Designs
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Screening Design Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Using Two Continuous Factors and One Categorical Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Using Five Continuous Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Creating a Screening Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Enter Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Enter Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
Choose a Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Display and Modify a Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
Specify Output Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
View the Design Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
Create a Plackett-Burman design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
iii
Analysis of Screening Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
Using the Screening Analysis Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Using the Fit Model Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5 Response Surface Designs
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
A Box-Behnken Design: The Tennis Ball Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
The Prediction Profiler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
A Response Surface Plot (Contour Profiler) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
Geometry of a Box-Behnken Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
Creating a Response Surface Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
Enter Responses and Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Choose a Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Specify Output Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
View the Design Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
6 Full Factorial Designs
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
The Five-Factor Reactor Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Analyze the Reactor Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
iv
Creating a Factorial Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Enter Responses and Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Select Output Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
Make the Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
7 Mixture Designs
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Mixture Design Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
The Optimal Mixture Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
The Simplex Centroid Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
Creating the Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Simplex Centroid Design Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
The Simplex Lattice Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
The Extreme Vertices Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Creating the Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
An Extreme Vertices Example with Range Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
An Extreme Vertices Example with Linear Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
Extreme Vertices Method: How It Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
The ABCD Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
Creating Ternary Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Fitting Mixture Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
Whole Model Tests and Analysis of Variance Reports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
Understanding Response Surface Reports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
A Chemical Mixture Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
Create the Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
Analyze the Mixture Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
The Prediction Profiler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
The Mixture Profiler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
A Ternary Plot of the Mixture Response Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
8 Discrete Choice Designs
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Create an Example Choice Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Analyze the Example Choice Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
Design a Choice Experiment Using Prior Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
Administer the Survey and Analyze Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
Initial Choice Platform Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
Find Unit Cost and Trade Off Costs with the Profiler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
9 Space-Filling Designs
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
Introduction to Space-Filling Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
Sphere-Packing Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
Creating a Sphere-Packing Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
Visualizing the Sphere-Packing Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
Latin Hypercube Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
Creating a Latin Hypercube Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
Visualizing the Latin Hypercube Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
Uniform Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
Comparing Sphere-Packing, Latin Hypercube, and Uniform Methods . . . . . . . . . . . . . . . . . . . . . . . . 206
Minimum Potential Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
Maximum Entropy Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
v
Gaussian Process IMSE Optimal Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
Borehole Model: A Sphere-Packing Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
Create the Sphere-Packing Design for the Borehole Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
Guidelines for the Analysis of Deterministic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
Results of the Borehole Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
10 Accelerated Life Test Designs
Designing Experiments for Accelerated Life Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
Overview of Accelerated Life Test Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
Using the ALT Design Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
Platform Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
11 Nonlinear Designs
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
Examples of Nonlinear Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
Using Nonlinear Fit to Find Prior Parameter Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
Creating a Nonlinear Design with No Prior Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
vi
Creating a Nonlinear Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Identify the Response and Factor Column with Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Set Up Factors and Parameters in the Nonlinear Design Dialog . . . . . . . . . . . . . . . . . . . . . . . . . . 244
Enter the Number of Runs and Preview the Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
Make Table or Augment the Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
Advanced Options for the Nonlinear Designer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
12 Taguchi Designs
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
The Taguchi Design Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
Taguchi Design Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
Analyze the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
Creating a Taguchi Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
Detail the Response and Add Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
Choose Inner and Outer Array Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
Display Coded Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
Make the Design Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
13 Augmented Designs
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
A D-Optimal Augmentation of the Reactor Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
Analyze the Augmented Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
Creating an Augmented Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
Replicate a Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
Add Center Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
Creating a Foldover Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
Adding Axial Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
Adding New Runs and Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
Special Augment Design Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
Save the Design (X) Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
Modify the Design Criterion (D- or I- Optimality) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
Select the Number of Random Starts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
Specify the Sphere Radius Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
Disallow Factor Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
14 Prospective Sample Size and Power
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
Launching the Sample Size and Power Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
One-Sample and Two-Sample Means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
Single-Sample Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
Sample Size and Power Animation for One Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
Two-Sample Means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
k-Sample Means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
One Sample Standard Deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
One Sample Standard Deviation Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
One-Sample and Two-Sample Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
One Sample Proportion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
Two Sample Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302
Counts per Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
Counts per Unit Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306
Sigma Quality Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
Sigma Quality Level Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
Number of Defects Computation Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308
vii
Reliability Test Plan and Demonstration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308
Reliability Test Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308
Reliability Demonstration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
Index
Design of Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
viii
Credits and Acknowledgments
Origin
JMP was developed by SAS Institute Inc., Cary, NC. JMP is not a part of the SAS System, though portions
of JMP were adapted from routines in the SAS System, particularly for linear algebra and probability
calculations. Version 1 of JMP went into production in October 1989.
Credits
JMP was conceived and started by John Sall. Design and development were done by John Sall, Chung-Wei
Ng, Michael Hecht, Richard Potter, Brian Corcoran, Annie Dudley Zangi, Bradley Jones, Craige Hales,
Chris Gotwalt, Paul Nelson, Xan Gregg, Jianfeng Ding, Eric Hill, John Schroedl, Laura Lancaster, Scott
McQuiggan, Melinda Thielbar, Clay Barker, Peng Liu, Dave Barbour, Jeff Polzin, John Ponte, and Steve
Amerige.
In the SAS Institute Technical Support division, Duane Hayes, Wendy Murphrey, Rosemary Lucas, Win
LeDinh, Bobby Riggs, Glen Grimme, Sue Walsh, Mike Stockstill, Kathleen Kiernan, and Liz Edwards
provide technical support.
Nicole Jones, Kyoko Keener, Hui Di, Joseph Morgan, Wenjun Bao, Fang Chen, Susan Shao, Yusuke Ono,
Michael Crotty, Jong-Seok Lee, Tonya Mauldin, Audrey Ventura, Ani Eloyan, Bo Meng, and Sequola
McNeill provide ongoing quality assurance. Additional testing and technical support are provided by Noriki
Inoue, Kyoko Takenaka, and Masakazu Okada from SAS Japan.
Bob Hickey and Jim Borek are the release engineers.
The JMP books were written by Ann Lehman, Lee Creighton, John Sall, Bradley Jones, Erin Vang, Melanie
Drake, Meredith Blackwelder, Diane Perhac, Jonathan Gatlin, Susan Conaghan, and Sheila Loring, with
contributions from Annie Dudley Zangi and Brian Corcoran. Creative services and production was done by
SAS Publications. Melanie Drake implemented the Help system.
Jon Weisz and Jeff Perkinson provided project management. Also thanks to Lou Valente, Ian Cox, Mark
Bailey, and Malcolm Moore for technical advice.
Thanks also to Georges Guirguis, Warren Sarle, Gordon Johnston, Duane Hayes, Russell Wolfinger,
Randall Tobias, Robert N. Rodriguez, Ying So, Warren Kuhfeld, George MacKensie, Bob Lucas, Warren
Kuhfeld, Mike Leonard, and Padraic Neville for statistical R&D support. Thanks are also due to Doug
Melzer, Bryan Wolfe, Vincent DelGobbo, Biff Beers, Russell Gonsalves, Mitchel Soltys, Dave Mackie, and
Stephanie Smith, who helped us get started with SAS Foundation Services from JMP.
Acknowledgments
We owe special gratitude to the people that encouraged us to start JMP, to the alpha and beta testers of
JMP, and to the reviewers of the documentation. In particular we thank Michael Benson, Howard
x
Yetter (d), Andy Mauromoustakos, Al Best, Stan Young, Robert Muenchen, Lenore Herzenberg, Ramon
Leon, Tom Lange, Homer Hegedus, Skip Weed, Michael Emptage, Pat Spagan, Paul Wenz, Mike Bowen,
Lori Gates, Georgia Morgan, David Tanaka, Zoe Jewell, Sky Alibhai, David Coleman, Linda Blazek,
Michael Friendly, Joe Hockman, Frank Shen, J.H. Goodman, David Iklé, Barry Hembree, Dan Obermiller,
Jeff Sweeney, Lynn Vanatta, and Kris Ghosh.
Also, we thank Dick DeVeaux, Gray McQuarrie, Robert Stine, George Fraction, Avigdor Cahaner, José
Ramirez, Gudmunder Axelsson, Al Fulmer, Cary Tuckfield, Ron Thisted, Nancy McDermott, Veronica
Czitrom, Tom Johnson, Cy Wegman, Paul Dwyer, DaRon Huffaker, Kevin Norwood, Mike Thompson,
Jack Reese, Francois Mainville, and John Wass.
We also thank the following individuals for expert advice in their statistical specialties: R. Hocking and P.
Spector for advice on effective hypotheses; Robert Mee for screening design generators; Roselinde Kessels
for advice on choice experiments; Greg Piepel, Peter Goos, J. Stuart Hunter, Dennis Lin, Doug
Montgomery, and Chris Nachtsheim for advice on design of experiments; Jason Hsu for advice on multiple
comparisons methods (not all of which we were able to incorporate in JMP); Ralph O’Brien for advice on
homogeneity of variance tests; Ralph O’Brien and S. Paul Wright for advice on statistical power; Keith
Muller for advice in multivariate methods, Harry Martz, Wayne Nelson, Ramon Leon, Dave Trindade, Paul
Tobias, and William Q. Meeker for advice on reliability plots; Lijian Yang and J.S. Marron for bivariate
smoothing design; George Milliken and Yurii Bulavski for development of mixed models; Will Potts and
Cathy Maahs-Fladung for data mining; Clay Thompson for advice on contour plotting algorithms; and
Tom Little, Damon Stoddard, Blanton Godfrey, Tim Clapp, and Joe Ficalora for advice in the area of Six
Sigma; and Josef Schmee and Alan Bowman for advice on simulation and tolerance design.
For sample data, thanks to Patrice Strahle for Pareto examples, the Texas air control board for the pollution
data, and David Coleman for the pollen (eureka) data.
Translations
Trish O'Grady coordinates localization. Special thanks to Noriki Inoue, Kyoko Takenaka, Masakazu Okada,
Naohiro Masukawa and Yusuke Ono (SAS Japan); and Professor Toshiro Haga (retired, Tokyo University of
Science) and Professor Hirohiko Asano (Tokyo Metropolitan University) for reviewing our Japanese
translation; Professors Fengshan Bai, Xuan Lu, and Jianguo Li at Tsinghua University in Beijing, and their
assistants Rui Guo, Shan Jiang, Zhicheng Wan, and Qiang Zhao; and William Zhou (SAS China) and
Zhongguo Zheng, professor at Peking University, for reviewing the Simplified Chinese translation; Jacques
Goupy (consultant, ReConFor) and Olivier Nuñez (professor, Universidad Carlos III de Madrid) for
reviewing the French translation; Dr. Byung Chun Kim (professor, Korea Advanced Institute of Science and
Technology) and Duk-Hyun Ko (SAS Korea) for reviewing the Korean translation; Bertram Schäfer and
David Meintrup (consultants, StatCon) for reviewing the German translation; Patrizia Omodei, Maria
Scaccabarozzi, and Letizia Bazzani (SAS Italy) for reviewing the Italian translation. Finally, thanks to all the
members of our outstanding translation teams.
Past Support
Many people were important in the evolution of JMP. Special thanks to David DeLong, Mary Cole, Kristin
Nauta, Aaron Walker, Ike Walker, Eric Gjertsen, Dave Tilley, Ruth Lee, Annette Sanders, Tim Christensen,
Eric Wasserman, Charles Soper, Wenjie Bao, and Junji Kishimoto. Thanks to SAS Institute quality
assurance by Jeanne Martin, Fouad Younan, and Frank Lassiter. Additional testing for Versions 3 and 4 was
done by Li Yang, Brenda Sun, Katrina Hauser, and Andrea Ritter.
Also thanks to Jenny Kendall, John Hansen, Eddie Routten, David Schlotzhauer, and James Mulherin.
Thanks to Steve Shack, Greg Weier, and Maura Stokes for testing JMP Version 1.
Thanks for support from Charles Shipp, Harold Gugel (d), Jim Winters, Matthew Lay, Tim Rey, Rubin
Gabriel, Brian Ruff, William Lisowski, David Morganstein, Tom Esposito, Susan West, Chris Fehily, Dan
Chilko, Jim Shook, Ken Bodner, Rick Blahunka, Dana C. Aultman, and William Fehlner.
Technology License Notices
xi
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xii
Chapter 1
Introduction to Designing Experiments
A Beginner’s Tutorial
This tutorial chapter introduces you to the design of experiments (DOE) using JMP’s custom designer. It
gives a general understanding of how to design an experiment using JMP. Refer to subsequent chapters in
this book for more examples and procedures on how to design an experiment for your specific project.
Contents
About Designing Experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
My First Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
The Situation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Step 1: Design the Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Step 2: Define Factor Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Step 3: Add Interaction Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Step 4: Determine the Number of Runs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Step 5: Check the Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Step 6: Gather and Enter the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Step 7: Analyze the Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
Chapter 1 Introduction to Designing Experiments 3
About Designing Experiments
About Designing Experiments
Increasing productivity and improving quality are important goals in any business. The methods for
determining how to increase productivity and improve quality are evolving. They have changed from costly
and time-consuming trial-and-error searches to the powerful, elegant, and cost-effective statistical methods
that JMP provides.
Designing experiments in JMP is centered around factors, responses, a model, and runs. JMP helps you
determine if and how a factor affects a response.
My First Experiment
If you have never used JMP to design an experiment, this section shows you how to design the experiment
and how to understand JMP’s output.
Tip: The recommended way to create an experiment is to use the custom designer. JMP also provides
classical designs for use in textbook situations.
The Situation
Your goal is to find the best way to microwave a bag of popcorn. Because you have some experience with
this, it is easy to decide on reasonable ranges for the important factors:
• how long to cook the popcorn (between 3 and 5 minutes)
• what level of power to use on the microwave oven (between settings 5 and 10)
• which brand of popcorn to use (Top Secret or Wilbur)
When a bag of popcorn is popped, most of the kernels pop, but some remain unpopped. You prefer to have
all (or nearly all) of the kernels popped and no (or very few) unpopped kernels. Therefore, you define “the
best popped bag” based on the ratio of popped kernels to the total number of kernels.
A good way to improve any procedure is to conduct an experiment. For each experimental run, JMP’s
custom designer determines which brand to use, how long to cook each bag in the microwave and what
power setting to use. Each run involves popping one bag of corn. After popping a bag, enter the total
number of kernels and the number of popped kernels into the appropriate row of a JMP data table. After
doing all the experimental runs, use JMP’s model fitting capabilities to do the data analysis. Then, you can
use JMP’s profiling tools to determine the optimal settings of popping time, power level, and brand.
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My First Experiment
Step 1: Design the Experiment
The first step is to select DOE > Custom Design. Then, define the responses and factors.
Define the Responses: Popped Kernels and Total Kernels
There are two responses in this experiment:
• the number of popped kernels
• the total number of kernels in the bag. After popping the bag add the number of unpopped kernels to
the number of popped kernels to get the total number of kernels in the bag.
By default, the custom designer contains one response labeled
Figure 1.1 Custom Design Responses Panel
Y (Figure 1.1).
You want to add a second response to the Responses panel and change the names to be more descriptive:
1. To rename the
increase the number of popped kernels, leave the goal at
2. To add the second response (total number of kernels), click
menu that appears. JMP labels this response
3. Double-click
Y response, double-click the name and type “Number Popped.” Since you want to
Maximize.
Add Response and choose None from the
Y2 by default.
Y2 and type “Total Kernels” to rename it.
The completed Responses panel looks like Figure 1.2.
Figure 1.2 Renamed Responses with Specified Goals
Chapter 1 Introduction to Designing Experiments 5
My First Experiment
Define the Factors: Time, Power, and Brand
In this experiment, the factors are:
• brand of popcorn (Top Secret or Wilbur)
• cooking time for the popcorn (3 or 5 minutes)
• microwave oven power level (setting 5 or 10)
In the Factors panel, add
1. Click
Add Factor and select Categorical > 2 Level.
Brand as a two-level categorical factor:
2. To change the name of the factor (currently named
3. To rename the default levels (
Add
Time as a two-level continuous factor:
4. Click
Add Factor and select Continuous.
5. Change the default name of the factor (
6. Likewise, to rename the default levels (
L1 and L2), click the level names and type Top S ec r e t and Wilbur.
X2) by double-clicking it and typing Time.
–1 and 1) as 3 and 5, click the current level name and type in the
new value.
Add
Power as a two-level continuous factor:
7. Click
8. Change the name of the factor (currently named
9. Rename the default levels (currently named
Add Factor and select Continuous.
X3) by double-clicking it and typing Power.
-1 and 1) as 5 and 10 by clicking the current name and
typing. The completed Factors panel looks like Figure 1.3.
Figure 1.3 Renamed Factors with Specified Values
X1), double-click on its name and type Brand.
10. Click Continue.
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My First Experiment
Step 2: Define Factor Constraints
The popping time for this experiment is either 3 or 5 minutes, and the power settings on the microwave are
5 and 10. From experience, you know that
• popping corn for a long time on a high setting tends to scorch kernels.
• not many kernels pop when the popping time is brief and the power setting is low.
You want to constrain the combined popping time and power settings to be less than or equal to 13, but
greater than or equal to 10. To define these limits:
1. Open the Constraints panel by clicking the disclosure button beside the
Define Factor Constraints title
bar (see Figure 1.4).
2. Click the
Add Constraint button twice, once for each of the known constraints.
3. Complete the information, as shown to the right in Figure 1.4. These constraints tell the Custom
Designer to avoid combinations of
to change
<= to >= in the second constraint.
Power and Time that sum to less than 10 and more than 13. Be sure
The area inside the parallelogram, illustrated on the left in Figure 1.4, is the allowable region for the runs.
You can see that popping for 5 minutes at a power of 10 is not allowed and neither is popping for 3 minutes
at a power of 5.
Figure 1.4 Defining Factor Constraints
Step 3: Add Interaction Terms
You are interested in the possibility that the effect of any factor on the proportion of popped kernels may
depend on the value of some other factor. For example, the effect of a change in popping time for the
Wilbur popcorn brand could be larger than the same change in time for the Top Secret brand. This kind of
synergistic effect of factors acting in concert is called a two-factor interaction. You can examine all possible
two-factor interactions in your a priori model of the popcorn popping process.
1. Click
Interactions in the Model panel and select 2nd. JMP adds two-factor interactions to the model as
shown to the left in Figure 1.5.
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My First Experiment
In addition, you suspect the graph of the relationship between any factor and any response might be curved.
You can see whether this kind of curvature exists with a quadratic model formed by adding the second order
powers of effects to the model, as follows.
2. Click
Powers and select 2nd to add quadratic effects of the continuous factors, Power and Time.
The completed Model should look like the one to the right in Figure 1.5.
Figure 1.5 Add Interaction and Power Terms to the Model
Step 4: Determine the Number of Runs
The Design Generation panel in Figure 1.6 shows the minimum number of runs needed to perform the
experiment with the effects you’ve added to the model. You can use that minimum or the default number of
runs, or you can specify your own number of runs as long as that number is more than the minimum. JMP
has no restrictions on the number of runs you request. For this example, use the default number of runs, 16.
Click
Make Design to continue.
Figure 1.6 Model and Design Generation Panels
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My First Experiment
Step 5: Check the Design
When you click Make Design, JMP generates and displays a design, as shown on the left in Figure 1.7.
Note that because JMP uses a random seed to generate custom designs and there is no unique optimal
design for this problem, your table may be different than the one shown here. You can see in the table that
the custom design requires 8 runs using each brand of popcorn.
Scroll to the bottom of the Custom Design window and look at the Output Options area (shown to the
right in Figure 1.7. The
data table when it is created. Keep the selection at
in a random order.
Run Order option lets you designate the order you want the runs to appear in the
Randomize so the rows (runs) in the output table appear
Now click
Figure 1.7 Design and Output Options Section of Custom Designer
Make Table in the Output Options section.
The resulting data table (Figure 1.8) shows the order in which you should do the experimental runs and
provides columns for you to enter the number of popped and total kernels.
You do not have fractional control over the power and time settings on a microwave oven, so you should
round the power and time settings, as shown in the data table. Although this altered design is slightly less
optimal than the one the custom designer suggested, the difference is negligible.
Tip: Note that optionally, before clicking
Right
in the Run Order menu to have JMP present the results in the data table according to the brand. We
have conducted this experiment for you and placed the results, called
Sample Data folder installed with JMP. These results have the columns sorted from left to right.
Make Table in the Output Options, you could select Sort Left to
Popcorn DOE Results.jmp, in the
Chapter 1 Introduction to Designing Experiments 9
results from
experiment
scripts to
analyze data
My First Experiment
Figure 1.8 JMP Data Table of Design Runs Generated by Custom Designer
Step 6: Gather and Enter the Data
Pop the popcorn according to the design JMP provided. Then, count the number of popped and unpopped
kernels left in each bag. Finally, enter the numbers shown below into the appropriate columns of the data
table.
We have conducted this experiment for you and placed the results in the
JMP. To see the results, open
data.
The data table is shown in Figure 1.9.
Figure 1.9 Results of the Popcorn DOE Experiment
Popcorn DOE Results.jmp from the Design Experiment folder in the sample
Sample Data folder installed with
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My First Experiment
Step 7: Analyze the Results
After the experiment is finished and the number of popped kernels and total kernels have been entered into
the data table, it is time to analyze the data. The design data table has a script, labeled
the top left panel of the table. When you created the design, a standard least squares analysis was stored in
the
Model script with the data table.
Model, that shows in
1. Click the red triangle for
The default fitting personality in the model dialog is
Model and select Run Script.
Standard Least Squares. One assumption of
standard least squares is that your responses are normally distributed. But because you are modeling the
proportion of popped kernels it is more appropriate to assume that your responses come from a binomial
distribution. You can use this assumption by changing to a generalized linear model.
2. Change the Personality to
Logit, as shown in Figure 1.10.
Figure 1.10 Fitting the Model
Generalized Linear Model, Distribution to Binomial, and Link Function to
3. Click Run.
4. Scroll down to view the Effect Tests table (Figure 1.11) and look in the column labeled Prob>Chisq.
This column lists p-values. A low p-value (a value less than 0.05) indicates that results are statistically
significant. There are asterisks that identify the low p-values. You can therefore conclude that, in this
experiment, all the model effects except for
there is a strong relationship between popping time (
(
Brand), and the proportion of popped kernels.
Time*Time are highly significant. You have confirmed that
Time), microwave setting (Power), popcorn brand
Chapter 1 Introduction to Designing Experiments 11
p-values indicate significance.
Values with * beside them are
p-values that indicate the results
are statistically significant.
Prediction trace
for
Brand
predicted value
of the response
95% confidence
interval on the mean
response
Factor values (here, time = 4)
Prediction trace
for
Time
Prediction trace
for
Power
Disclosure icon to
open or close the
Prediction Profiler
My First Experiment
Figure 1.11 Investigating p-Values
To further investigate, use the Prediction Profiler to see how changes in the factor settings affect the
numbers of popped and unpopped kernels:
1. Choose
Profilers > Profiler from the red triangle menu on the Generalized Linear Model Fit title bar.
The Prediction Profiler is shown at the bottom of the report. Figure 1.12 shows the Prediction Profiler
for the popcorn experiment. Prediction traces are displayed for each factor.
Figure 1.12 The Prediction Profiler
2. Move the vertical red dotted lines to see the effect that changing a factor value has on the response. For
example, drag the red line in the
Time graph to the right and left (Figure 1.13).
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My First Experiment
Figure 1.13 Moving the Time Value from 4 to Near 5
As Time increases and decreases, the curved Time and Power prediction traces shift their slope and
maximum/minimum values. The substantial slope shift tells you there is an interaction (synergistic effect)
involving
Time and Power.
Furthermore, the steepness of a prediction trace reveals a factor’s importance. Because the prediction trace
for
Time is steeper than that for Brand or Power (see Figure 1.13), you can see that cooking time is more
important than the brand of popcorn or the microwave power setting.
Now for the final steps.
3. Click the red triangle icon in the Prediction Profiler title bar and select
4. Click the red triangle icon in the Prediction Profiler title bar and select
Desirability Functions.
Maximize Desirability. JMP
automatically adjusts the graph to display the optimal settings at which the most kernels will be popped
(Figure 1.14).
Our experiment found how to cook the bag of popcorn with the greatest proportion of popped kernels: use
Top Secret, cook for five minutes, and use a power level of 8. The experiment predicts that cooking at these
settings will yield greater than 96.5% popped kernels.
Chapter 1 Introduction to Designing Experiments 13
My First Experiment
Figure 1.14 The Most Desirable Settings
The best settings are the Top Secret brand, cooking time at 5, and power set at 8.
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My First Experiment
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