Jmp Doe Guide

"The real voyage of discovery consists not in seeking new landscapes, but in having new eyes." Marcel Proust

DESIGN OF EXPERIMENTS SAS Institute Inc. SAS Campus Drive Cary, NC 27513

JMP® Design of Experiments, Version 4 Copyright © 2000 by SAS Institute Inc., Cary, NC, USA ISBN: 1-58025-631-7 All rights reserved. Printed in the United States of America. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, or otherwise, without prior written permission of the publisher, SAS Institute Inc. Information in this document is subject to change without notice. The software described in this document is furnished under a license agreement and may be used or copied only in accordance with the terms of the agreement. It is against the law to copy the software on any medium except as specifically allowed in the license agreement. First printing, January 2000 JMP®, SAS®, and all other SAS Institute Inc. product or service names are registered trademarks of SAS Institute Inc. All trademarks above 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. Imageman® is a registered trademark or trademark of Data Techniques, Inc. All rights reserved. Microsoft Text-to-Speech Engine® is a registered trademark or trademark Microsoft Corporation. All rights reserved. Installer VISE TM , Updater VISE®, and MindExpander® are trademerks of MindVision Inc. All rights reserved worldwide. Install Shield® is a registered trademark of InstallShield Software Corporation. All rights reserved. Mercutio MDEF® is a registered trademark or trademark of Digital Alchemy, Ramon M. Felciano. All rights reserved.

JMP Design Of Experiments Contents Credits and Acknowledgments ............................................................................................v Chapter 1 Design of Experiments (DOE) ....................................................................... 1 DOE Choices ................................................................................................................... 3 A Simple DOE Example ................................................................................................. 6 The DOE Dialog.............................................................................................................. 7 The JMP DOE Data Table............................................................................................. 11 DOE Utility Commands ................................................................................................ 12 Chapter 2 Introduction to Custom Designs ................................................................. 17 Getting Started ............................................................................................................... 19 Modify a Design Interactively ....................................................................................... 23 Introducing the Prediction Profiler................................................................................ 24 Routine Screening Using Custom Designs ................................................................... 29 How the Custom Designer Works ................................................................................. 32 Chapter 3 Custom Design: Beyond the Textbook ....................................................... 33 Custom Situations ......................................................................................................... 35 Flexible Block Sizes ...................................................................................................... 36 Response Surface Model with Categorical Factors ....................................................... 38 Fixed Covariate Factors................................................................................................. 43 Mixtures with Nonmixture Factors ............................................................................... 45 Factor Constraints ......................................................................................................... 48 Chapter 4 Screening Designs ....................................................................................... 53 Screening Design Types ................................................................................................ 55 A Screening Example .................................................................................................... 58 Loading and Saving Responses and Factors (Optional)................................................ 66 A Simple Effect Screening Analysis ............................................................................. 67 Chapter 5 Response Surface Designs ........................................................................... 69 Response Surface Designs............................................................................................. 71 A Box-Behnken Design: The Tennis Ball Example ..................................................... 76

Chapter 6 Full Factorial Designs .................................................................................. 85 The Factorial Dialog...................................................................................................... 87 The Five-Factor Reactor Example................................................................................. 88 Chapter 7 Taguchi Designs ........................................................................................... 97 The Taguchi Design Approach ..................................................................................... 99 Taguchi Design Example .............................................................................................. 99 Analyze the Byrne-Taguchi Data ................................................................................ 103 Chapter 8 Mixture Designs ......................................................................................... 105 The Mixture Design Dialog ......................................................................................... 107 Mixture Designs .......................................................................................................... 108 Extreme Vertices Design for Constrained Factors ...................................................... 113 Adding Linear Constraints to Mixture Designs........................................................... 114 Ternary and Tetrary Plots............................................................................................ 115 Fitting Mixture Designs............................................................................................... 116 Chemical Mixture Example......................................................................................... 118 Plotting a Mixture Response Surface .......................................................................... 119 Chapter 9 Augmented Designs ................................................................................... 121 The Augment Design Interface ................................................................................... 123 The Reactor Example Re-visited ................................................................................. 126 Chapter 10 Prosective Power and Sample Size ......................................................... 135 Prospective Power Analysis ........................................................................................ 137 Launch the Sample Size and Power facility ................................................................ 137 References ...................................................................................................................... 145 Index ............................................................................................................................... 149

Origin JMP was developed by SAS Institute Inc., Cary, N.C. JMP is not a part of the SAS System and is not as portable as SAS. A SAS add-on product called SAS/INSIGHT is related to JMP in some ways but has different conventions and capabilities. 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 was done by John Sall, Katherine Ng, Michael Hecht, Richard Potter, Brian Corcoran, Annie Dudley, Bradley Jones, Xan Gregg, Eric Wasserman, Charles Soper, and Kevin Hardman. Ann Lehman coordinated product development, production, quality assurance, and documentation. In the SAS Institute Technical Support division, Ryan Gilmore, Maureen Hayes, Craig Devault, Toby Trott, and Peter Ruzza provide technical support and conducted test site administration. Statistical technical support is provided by Duane Hayes, Kathleen Kiernan, and Annette Sanders. Nicole Jones and Jianfeng Ding provide ongoing quality assurance. Additional testing and technical support is done by Kyoko Takenaka and Noriki Inoue from SAS Japan. Sales and marketing is headed by Colleen Jenkins and includes Dianne Nobles, William Gjertsen, Chris Brown, Carolyn Durst, Mendy Clayton, Bob Hickey, David Sipple, Barbara Droschak, Lisa Rohloff, Bob McCall, Chuck Boiler, Nick Zagone and Bonnie Rigo. Additional support is provided by Kathy Jablonski and Jean Davis. The JMP manuals were written by Ann Lehman, John Sall, Bradley Jones, and Erin Vang with contributions from Annie Dudley and Brian Corcoran. Editing was done by Lee Bumgarner, Brad Kellam, and Lee Creighton, design and production by Creative Solutions. Lee Creighton implemented the online help system and online documentation with contribution from Timothy Christensen. Special thanks to Jim Goodnight for supporting a product outside the usual traditions and to Dave DeLong for valuable ideas and advice on statistical and computational matters. Thanks also to Robert N. Rodriguez, Ying So, Duane Hayes, Mark Bailey, Donna Woodward, and Mike Stockstill for statistical editorial support and statistical QC advice. Thanks to Georges Guirguis, Warren Sarle, Randall Tobias, Gordon Johnston, Ying So, Wolfgang Hartmann, Russell Wolfinger, and Warren Kuhfeld for statistical R&D support. 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 Yetter, Al Best, Stan Young, Robert Muenchen, Lenore Herzenberg, Larry Sue, Ramon Leon, Tom Lange, Homer Hegedus, Skip Weed, Michael Emptage, Pat Spagan, John Frei, Paul Wenz, Mike Bowen, Lori Gates, Georgia Morgan, David Coleman, Linda Blazek, Michael Friendly, Joe Hockman, Frank Shen, J.H. Goodman, David Ikle, Lou Valente, Robert Mee, Barry Hembree, Dan Obermiller, Lynn Vanatta, and Kris Ghosh. Also, we thank Dick DeVeaux, Gray McQuarrie, Robert Stein, George Fraction, Al Fulmer, Cary Tuckfield, Ron Thisted, Donna Fulenwider, Nancy McDermott, Veronica Czitrom, Tom Johnson, Avigdor Cahaner, and Andy Mauromoustakos.

vi

We also thank the following individuals for expert advice in their statistical specialties: R. Hocking and P. Spector for advice on effective hypotheses; 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 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; Clay Thompson for advice on contour plotting algorithms. 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. Past Support Many people were important in the evolution of JMP. Special thanks Jeffrey Perkinson, Mary Cole, Kristin Nauta, Aaron Walker, Ike Walker, Eric Gjertsen, Dave Tilley, Curt Yeo, Patricia Moell, Patrice Cherry, Mike Pezzoni, Mary Ann Hansen, Ruth Lee, Russell Gardner, and Patsy Poole. SAS Institute quality assurance by Jeanne Martin, Fouad Younan, Jeff Schrilla, Jack Berry, Kari Richardson, Jim Borek, Kay Bydalek, and Frank Lassiter. Additional testing for Versions 3 and 4 was done by Li Yang, Brenda Sun, Katrina Hauser, and Andrea Ritter. Thanks to Walt Martin for Postscript support in documentation production. Also thanks to Jenny Kendall, Elizabeth Shaw, and John Hansen, Eddie Routten, David Schlotzhauer, John Boling, and James Mulherin, Thanks to Steve Shack, Greg Weier, and Maura Stokes for testing Version 1. Additional editorial support was given by Marsha Russo, Dea Zullo, and Dee Stribling. Thanks for support from Morgan Wise, Frederick Dalleska, Stuart Janis, Charles Shipp, Harold Gugel, Jim Winters, Matthew Lay, Tim Rey, Rubin Gabriel, Brian Ruff, William Lisowski, David Morganstein, Tom Esposito, Susan West, Chris Fehily, Dan Chilko, Jim Shook, Bud Martin, Hal Queen, Ken Bodner, Rick Blahunka, Dana C. Aultman, and William Fehlner.

Technology License Notices JMP software contains portions of the file translation library of MacLinkPlus, a product of DataViz Inc., 55 Corporate Drive, Trumbull, CT 06611, (203) 268-0030. JMP for the Power Macintosh was compiled and built using the CodeWarrior C compiler from MetroWorks Inc. SAS INSTITUTE INC.’S LICENSORS MAKE NO WARRANTIES, EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, REGARDING THE SOFTWARE. SAS INSTITUTE INC.’S LICENSORS DO NOT WARRANT, GUARANTEE OR MAKE ANY REPRESENTATIONS REGARDING THE USE OR THE RESULTS OF THE USE OF THE SOFTWARE IN TERMS OF ITS CORRECTNESS, ACCURACY, RELIABILITY, CURRENTNESS OR OTHERWISE. THE ENTIRE RISK AS TO THE RESULTS AND PERFORMANCE OF THE SOFTWARE IS ASSUMED BY YOU. THE EXCLUSION OF IMPLIED WARRANTIES IS NOT PERMITTED BY SOME STATES. THE ABOVE EXCLUSION MAY NOT APPLY TO YOU. IN NO EVENT WILL SAS INSTITUTE INC.’S LICENSORS AND THEIR DIRECTORS, OFFICERS, EMPLOYEES OR AGENTS ( COLLECTIVELY SAS INSTITUTE INC.’S LICENSOR) BE LIABLE TO YOU FOR ANY CONSEQUENTIAL, INCIDENTAL OR INDIRECT DAMAGES (INCLUDING DAMAGES FOR LOSS OF BUSINESS PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, AND THE LIKE) ARISING OUT OF THE USE OR INABILITY TO USE THE SOFTWARE EVEN IF SAS INSTITUTE INC.’S LICENSOR’S HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. BECAUSE SOME STATES DO NOT ALLOW THE EXCLUSION OR LIMITATION OF LIABILITY FOR CONSEQUENTIAL OR INCIDENTAL DAMAGES, THE ABOVE LIMITATIONS MAY NOT APPLY TO YOU. SAS INSTITUTE INC.’S LICENSOR’S LIABILITY TO YOU FOR ACTUAL DAMAGES FOR ANY CAUSE WHATSOEVER, AND REGARDLESS OF THE FORM OF THE ACTION (WHETHER IN CONTRACT, TORT (INCLUDING NEGLIGENCE), PRODUCT LIABILITY OR OTHERWISE), WILL BE LIMITED TO $50.

1

The use of statistical methods in industry is increasing. Arguably, the most cost beneficial of these methods for quality and productivity improvement is statistical design of experiments. A trial-and-error search for the vital few factors that most affect quality is costly and time consuming. Fortunately, researchers in the field of experimental design have invented powerful and elegant ways of making the search process fast and effective. The DOE platform in JMP is a tool for creating designed experiments and saving them in a JMP data table. JMP supports two ways to make a designed experiment. The first way is to let JMP build a new design that both matches the description of your engineering problem and remains within your budget for time and material. Use the Custom and Augment designers to create these tailor-made designs. The second way is to choose a pre-formulated design from a list of designs. JMP groups these lists of designs into several types differing by problem type and research goal. For example, the Screening designer provides a list of designs suitable for doing screening experiments. The Response Surface, Taguchi, and Mixture designers also involve choosing the design you want from a list. Each of these two approaches has its advantages. Custom designs are general purpose and flexible. Custom designs are also fine for routine factor screening or response optimization. For problems that are not textbook, custom designs are the only alternative. On the other hand, when you know exactly the design you want, it is convenient to select it from a list. This chapter briefly describes each of the design types, shows how to use the DOE dialog to enter your factors and responses, and points out the special features of a JMP design data table.

1 JMP DOE

Chapter 1 Design of Experiments (DOE)

2

Chapter 1 Contents DOE Choices .............................................................................................................................. 3 Custom Design .................................................................................................................... 4 Screening Design ................................................................................................................. 4 Response Surface Design .................................................................................................... 4 Full Factorial Design ........................................................................................................... 5 Taguchi Arrays .................................................................................................................... 5 Mixture Design.................................................................................................................... 5 Augment Design.................................................................................................................. 5 Sample Size and Power ....................................................................................................... 6 A Simple DOE Example............................................................................................................. 6 The DOE Dialog ......................................................................................................................... 7 Entering Responses ............................................................................................................. 8 Entering Factors................................................................................................................... 9 Select a Design Type ......................................................................................................... 10 Modify a Design ................................................................................................................ 10 The JMP DOE Data Table........................................................................................................ 11 DOE Utility Commands ........................................................................................................... 12

Chapter 1 Design of Experiments

3

The DOE platform in JMP is an environment for describing the factors, responses and other specifications, creating a designed experiment, and saving it in a JMP table. When you select the DOE tab on the JMP Starter window, you see the list of design command buttons shown on the tab page as in Figure 1.1. Alternatively, you can choose commands from the DOE main menu shown to the right. Figure 1.1 The DOE JMP Starter Tab

Note that the DOE tab in the JMP Starter window tells what each command does. The specific design types are described briefly in the next sections, and covered in detail by the following chapters in this book.

1 JMP DOE

DOE Choices

4

Chapter 1 Design of Experiments

Custom Design Custom designs give the most flexibility of all design choices. The Custom designer gives you the following options: ❿

continuous factors

❿

categorical factors with arbitrary numbers of levels

❿

mixture ingredients

❿

covariates (factors that already have unchangable values and design around them)

❿

blocking with arbitrary numbers of runs per block

❿

interaction terms and polynomial terms for continuous factors

❿

inequality constraints on the factors

❿

choice of number of experimental runs to do, which can be any number greater than or equal to the number of terms in the model.

After specifying all your requirements, this design solution generates a D-optimal design for those requirements.

Screening Design As the name suggests, screening experiments “separate the wheat from the chaff.” The wheat is the group of factors having a significant influence on the response. The chaff is the rest of the factors. Typically screening experiments involve many factors. The Screening designer supplies a list of popular screening designs for 2 or more factors. Screening factors can be continuous or categorical with two or three levels. The list of screening designs also includes designs that group the experimental runs into blocks of equal sizes where the size is a power of two.

Response Surface Design Response Surface Methodology (RSM) is an experimental technique invented to find the optimal response within the specified ranges of the factors. These designs are capable of fitting a second order prediction equation for the response. The quadratic terms in these equations model the curvature in the true response function. If a maximum or minimum exists inside the factor region, RSM can find it. In industrial applications, RSM designs involve a small number of factors. This is because the required number of runs increases dramatically

Chapter 1 Design of Experiments

5

Full Factorial Design A full factorial design contains all possible combinations of a set of factors. This is the most conservative design approach, but it is also the most costly in experimental resources. The Full Factorial designer supports both continuous factors and categorical factors with arbitrary numbers of levels.

Taguchi Arrays The goal of the Taguchi Method is to find control factor settings that generate acceptable responses despite natural environmental and process variability. In each experiment, Taguchi’s design approach employs two designs called the inner and outer array. The Taguchi experiment is the cross product of these two arrays. The control factors, used to tweak the process, form the inner array. The noise factors, associated with process or environmental variability, form the outer array. Taguchi’s Signal-to-Noise Ratios are functions of the observed responses over an outer array. The Taguchi designer in JMP supports all these features of the Taguchi method. The inner and outer array design lists use the traditional Taguchi orthogonal arrays such as L4, L8, L16, and so forth.

Mixture Design The Mixture designer lets you define a set of factors that are ingredients in a mixture. You choose among several classical mixture design approaches, such as simplex, extreme vertices, and lattice. For the extreme vertices approach you can supply a set of linear inequality constraints limiting the geometry of the mixture factor space.

Augment Design The Augment designer gives the following four choices for adding new runs to existing design: ❿

add center points

❿

replicate the design a specified number of times

❿

create a foldover design

❿

add runs to the design using a model, which can have more terms than the original model.

1 JMP DOE

with the number of factors. The Response Surface designer in JMP lists well-known RSM designs for two to eight continuous factors. Some of these designs also allow blocking.

6

Chapter 1 Design of Experiments

The last choice (adding runs to a design) is particularly powerful. You can use this choice to achieve the objectives of response surface methodology by changing a linear model to a full quadratic model and adding the necessary number of runs. For example, suppose you start with a two-factor, two-level, four-run design. If you add quadratic terms to the model and five new points, JMP generates the 3 by 3 full factorial as the optimal augmented design.

Sample Size and Power The Sample Size and Power facility computes power, sample size, or the effect size you want to detect, for a given alpha and error standard deviation. You supply two of these values and the Sample Size and Power feature computes the third. If you supply only one of these values, the result is a plot of the other two. This feature is available for the single sample, two sample, and k sample situations.

A Simple DOE Example The following example demonstrates the interface for choosing designs from a list. It introduces the JMP DOE dialog that lets you ❿

enter factors and responses

❿

choose a design

❿

modify a design

❿

generate a JMP table that contains the design runs.

Suppose an engineer wants to investigate a process that uses an electron beam welding machine to join two parts. The engineer fits the two parts into a welding fixture that holds them snugly together. A voltage applied to a beam generator creates a stream of electrons that heats the two parts, causing them to fuse. The ideal depth of the fused region is 0.17 inches. The engineer wants to study the welding process to determine the best settings for the beam generator to produce the desired depth in the fused region.

For this study, the engineer wants to explore the following three inputs, which are the factors for the study: Operator, two technicians who operate the welding machine.

Chapter 1 Design of Experiments

7

Rotation Speed, which is the speed at which the part rotates under the beam.

After each processing run, the engineer cuts the part in half. This reveals an area where the two parts have fused. The Length of this fused area is the depth of penetration of the weld. This depth of penetration is the response for the study. The goals of the study are ❿

find which factors affect the depth of the weld

❿

quantify those effects

❿

find specific factor settings that predict a weld depth of 0.17 inches.

The next sections show how to define this study in JMP with the DOE dialog

The DOE Dialog When you first select any command from the DOE menu, the DOE dialog appears. It has two basic panels, as illustrated by the dialog shown in Figure 1.2. ❿

The Responses panel has a single default response. You can enter as many responses as you want, and designate response goals as Maximize, Minimize, or Match Target. A response may also have no defined goal. The DOE platform accepts only numeric responses.

❿

The Factors panel requires that you enter one or more factors. The appearance of the Factors panel depends on the DOE command you select. For the 2-level design panel shown in Figure 1.2, enter the number of Continuous, 2-Level, or 3-level factors you want and click Add. Factor panels for other types of design are shown in more detail in the following chapters that describe the specific design types.

The results when you click Continue depend on the type of design. There are examples of each design type shown in the chapters that follow. For simplicity, this example uses the Screening designer. Note that the Responses and Factors panels have disclosure buttons so that you can close them. This lets you simplify the dialog when you are ready to Continue.

1 JMP DOE

Beam Current, which is a current that affects the intensity of the beam.

8

Chapter 1 Design of Experiments

Figure 1.2 The DOE Design Experiment Dialog For a Screening Design

Responses Panel Enter response and edit response names. Define response goal: Target, Min, Max, or None.

Factors Panel Enter Factors and click Add. Edit Factors names.

Click to see available designs.

Entering Responses By default, The Responses panel in the DOE dialog appears with one response (named Y) that has Maximize as its goal. There are several things you can do in this panel: ❿

Add an additional response with a specific goal type using selections from the Add Response popup menu.

❿

Add N additional responses with the N Responses button. The default goal is maximize.

❿

Specify goals appropriate for each goal type.

To continue with the welding example open the Responses panel if it is not already showing. Note that there is a single default response called Y. Change the default response as follows: 1) double click to highlight the response name and change it to Depth (In.).

Chapter 1 Design of Experiments

3) Click the Lower Bound, Upper Bound, areas and enter 0.12 as the target value, 0.22 as a minimum and maximum acceptable values.

Entering Factors Next enter factors into the Factors panel, which shows beneath the Responses panel. Design factors have different roles that depend on design type. The Factors panel reflects roles appropriate for the design you choose. The screening design accepts either continuous or categorical factors. This example has one categorical factor (Operator) and two continuous factors (Speed and Current). Enter 1 in the 2-Level Categorical text box and click Add. then click. Enter 2 in the Continuous text box and click Add. These three factors appear with default names (X1, X2, and X3) and the default values shown here. The factor names and values are editable fields. Double click on these fields to enter new names and values. For this example, use Mary and John as values for the categorical factor called Operator. Name the continuous factors Speed and Current. High and low values for Speed are 3 and 5 rpm. Values for Current are 150 and 165 amps. After you enter the response, the factors, and edit their values (optional), click Continue.

1 JMP DOE

2) The default goal is Maximize, but this process has a target value of 0.17 inches with a lower bound of 0.12 and an upper bound of 0.22. Click on the Goal text edit area and choose Match Target from the popup menu, as shown here.

9

10

Chapter 1 Design of Experiments

Select a Design Type When you click Continue, the next section of the design dialog unfolds. This Choose a Design panel is specific to the Screening designer. Other design types work differently at this stage. Details for each are in the following chapters. To reproduce the example shown here, click on Full Factorial in the list of designs to select it. The next section discusses additional steps you take in the DOE dialog to give JMP special instructions about details of the design. If necessary you can return (Backup) to the list of designs and select a different design. After you select a design type, click Continue again and interact with the Display and Modify Design panel to tailor the design. These detail options are different for each type of design.

Modify a Design Special features for screening designs include the ability to list the Aliasing of Effects, Change Generating Rules for aliasing, and view the Coded Design. A standard feature for all designs lets you specify the Run Order with selections from the run order popup menu. These features are used in examples and discussed in detail in the following chapters. When the design details are complete, click Make Table to create a JMP table that contains the specified design.

Chapter 1 Design of Experiments

11

The JMP DOE Data Table The example in the discussion above is for a factorial design with one 2-level categorical and two continuous factors. When you click Make Table, the JMP table in Figure 1.3 appears. The table uses the names for responses, factors, and levels assigned in the DOE dialog panels. The Pattern variable shows the coded design runs. This data table is called DOE Example 1.jmp in the Design Experiment folder in the sample data. Figure 1.3 The Generated DOE JMP Data Table

The table panels show table properties automatically created by the DOE platform: ❿

The name of the table is the design type that generated it.

❿

A table variable called Design also shows the design type. You can edit this table variable to further document the table, or you can create new table variables.

❿

A script to generate the analysis model is saved with the table. The icon labeled Model is a Table Property that runs a script that generates a Model Specification dialog with the analysis specification for the design type you picked. In this example the Model Specification dialog shows a single response, Depth (In.), three main effects, Operator, Speed, and Current, and all two factor interactions.

1 JMP DOE

Note: All dialogs have a Backup button that returns you to the previous stage of the design generation, where you can change the design type selection.

12

Chapter 1 Design of Experiments

Figure 1.4 The Model Specification dialog Generated by the DOE Dialog

DOE Utility Commands The DOE dialog has a number of efficiency features accessible using the popup menu on the Design Experiment title bar. Most of these features are for saving and loading information about variables. This is handy when you plan several experiments using the same factors and responses. There are examples of each feature in the list below. Many of the DOE case studies later in this manual also show how to benefit from these utilities. Save Responses

The Save Responses command creates a JMP table from a

Chapter 1 Design of Experiments

13

This example shows a DOE dialog for four responses with a variety of response goals, and the JMP table that contains the response information. Load Responses

If the responses and response goals are in a JMP table as described previously, you can use that table to complete the DOE dialog for an experiment. When the responses table you want is open and is the current table, the Load Responses command copies the response names and goals into the DOE dialog. If there is no response table open, Load Responses displays the Open File dialog for you to open the table you want to use. Save Factors

If an experiment has many factors, it can take time to enter the names and values for each factor. After you finish you can use the Save Factors command to save your work, so you only have to do this job once. The Save Factors command creates a JMP data table that contains the information in a completed factor list. The table has a column for each factor and a row for each factor level. As an example, suppose you entered the information showing in the dialog to the right. Save Factors produces the data table shown below. The columns of this table have a Column

1 JMP DOE

completed DOE dialog. The table has a row for each response with a column called Response Name that identifies them. Four additional columns identify response goals to the DOE facility: Lower Limit, Upper Limit, Response Goal, and an Importance weight.

14

Chapter 1 Design of Experiments

Property called Design Role, that identifies them as DOE factors to the DOE facility, and tells what kind of factors they are (continuous, categorical, blocking, and so on.). You can also create a factors table by keying data into an empty table, but you have to assign each column its factor type. Use the New Property menu in the Column Info dialog and select Design Role. Then choose the appropriate design role from the popup menu on the design role column property tab page. Load Factors

If the factors and levels for an experiment are in a JMP table as described previously, you can use that table to complete the DOE dialog for an experiment. If the factors table you want is open and is the current table, the Load Factors command copies the factor names, values, and factor types into the DOE dialog. If there is no factor table open, Load Factors displays the Open File dialog for you to open the factors table you want to use. Save Constraints

Entering constraints on continuous factors is another example of work you only want to do once. In the next example, there are three variables, X1, X2, and X3, with three linear constraints. The Save Constraints command creates a JMP table that contains the information you enter into a constraints panel like the one shown here. There is a columns for each constraint with a column property called Constraint State that identifies them as constraints (< or >) to the DOE facility. There is a row for each variable and an additional row that has the inequality condition for each variable. Load Constraints

If the responses and response goals are in a JMP table as described previously, you can use that table to complete the DOE dialog for an experiment. When the responses table you want is open and is the current table, the Load Constraints command copies the

Chapter 1 Design of Experiments

15

response names and goals into the DOE dialog. If there is no response table open, Load Set Random Seed

The Custom designer begins the design process with a random number. After a design is complete the Set Random Number command displays a dialog that shows the generating seed for that design. On this dialog you can set that design to run again, or continue with a new random number. Simulate Responses

When you check Simulate Response, that item shows as checked for the current design only. It adds simulated response values to the JMP design data table for custom and augmented designs.

1 JMP DOE

Responses displays the Open File dialog for you to open the table you want to use.

17

Chapter 2 Introduction to Custom Designs

❿

You can let JMP build a design for your specific problem that is consistent with your resource budget.

❿

You can choose a predefined design from one of the design catalogs, which are grouped by problem type.

create design to solve a problem

choose from catalogues of listed designs

modify any design

The Custom designer supports the first of these approaches. You can use it for routine factor screening, response optimization, and mixture problems. Also, the custom designer can find designs for special conditions not covered in the lists of predefined designs. This chapter introduces you to the Custom designer. It shows how to use the Custom Design interface to build a design using this easy step-by-step approach: Key engineering steps: process knowledge and engineering judgement are important.

Describe Identify factors and responses.

Design Compute design for maximum infromation from runs.

Fit

Collect Use design to set factors; measure responses for each run.

Compute best fit of mathematical model to data from test runs.

Predict Use model to find best factor settings for on-target responses and minimum variability.

Key mathematical steps: appropriate computer-based tools are empowering.

Chapter 3, “Custom Design: Beyond the Textbook," uses a case study approach to introduce the advanced capabilities of the Custom Design personality.

2 Customized I

The DOE platform in JMP has the following two approaches for building an experimental design:

18

Chapter 2 Contents Getting Started .......................................................................................................................... 19 Define Factors in the Factors Panel ................................................................................... 19 Describe the Model in the Model Panel ............................................................................ 20 The Design Generation Panel............................................................................................ 20 The Design Panel and Output Options .............................................................................. 21 Make Table........................................................................................................................ 22 Modify a Design Interactively .................................................................................................. 23 Introducing the Prediction Variance Profiler ........................................................................... 24 A Quadratic Model ............................................................................................................ 24 A Cubic Model .................................................................................................................. 26 Routine Screening Using Custom Designs ............................................................................... 28 Main Effects Only ............................................................................................................. 28 All Two-Factor Interactions Involving Only One Factor.................................................. 30 All Two-Factor Interactions .............................................................................................. 31 How the Custom Designer Works ............................................................................................ 32

Chapter 2 Custom Designs

19

Getting Started The purpose of this chapter is to guide you through the interface of the Custom Design personality. You interact with this facility to describe your experimental situation, and JMP creates a design that fits your requirements. The Custom Design interface has these key steps:

2) Use the Factors panel to name and describe the types of factors you have. 3) Enter factor constraints, if there are any. 4) Choose a model. 5) Modify the sample size alternatives. 6) Choose the run order. 7) Optionally, add center points and replicates. You can use the custom design dialog to enter main effects, then add interactions, and specify center points and replicates.

Define Factors in the Factors Panel When you select Custom Design from the DOE menu, or from the DOE tab on the JMP Starter, the dialog on the right in Figure 2.1 appears. One way to enter factors is to click Add N Factors text edit box and enter the number of continuous factors you want. If you want other kinds of factors click Add Factor and select a factor type: Continuous, Categorical, Blocking, Covariate, Mixture, or Constant. When you finish defining factors, Click Continue in the Factors panel to proceed to the next step.

2 Customized I

1) Enter and name one or more responses, if needed. The DOE dialog always begins with a single response, called Y, and the Response panel is closed by default.

20

Chapter 2 Custom Designs

Figure 2.1 Select Custom Design and Enter Factors

Describe the Model in the Model Panel When you click Continue, the Model panel initially appears with only the main effects corresponding to the factors you entered. Next, you might want to enter additional effects to estimate. That is, if you do not want to limit your model to main effects, you can add factor interactions or powers of continuous factors to the model. This simple example has two continuous factors, X1 and X2. When you click Continue, the current Model panel appears with only those factors, as shown here. The Model panel has buttons for you to add specific factor types to the model. For example, when you select 2nd from the Interaction popup menu, the X1*X2 interaction term is added to the model effects.

The Design Generation Panel As you add effects to the model, the Design Generation panel shows the minimum number of runs needed to perform the experiment. It also shows alternate numbers of runs, or lets

Chapter 2 Custom Designs

21

you choose your own number of runs. Balancing the cost of each run with the information gained by extra runs you add is a judgment call that you control. The Design Generation panel has the following radio buttons:

Default is a custom design suggestion for the number of runs. This value is based on heuristics for creating balanced designs with a minimum of additional runs above the minimum. Compromise is a second suggestion that is more conservative than the Default. Its value is generally between Default and Grid. Grid, in most cases, shows the number of points in a full-factorial design. Exceptions are for mixture and blocking designs. Generally Grid is unnecessarily large and is included as an options for reference and comparison. User Specified highlights the Number of Runs text box. You key in a number of runs that is at least the minimum. When the Design Generation panel is the way you want it, click Make Design to see the factor design layout, the Design panel, appended to the Model panel in the DOE dialog.

The Design Panel and Output Options Before you create a JMP data table of design runs you can use the Run Order option to designate the order you want the runs to appear in the JMP data table when it is created. If you select Keep the Same, the rows (runs) in the JMP table appear as they show in the Design panel. Alternatively, you can sort the table columns or randomize the runs.

2 Customized I

Minimum is the number of terms in the design model. The resulting design is saturated (no degrees of freedom for error). This is the most risky choice. Use it only when the cost of extra runs is prohibitive.

22

Chapter 2 Custom Designs

There are edit boxes to request additional runs at the center points be added, and to request rows that replicate the design (including any additional center points). Note: You can double-click any title bar to change its text. It can be helpful to give your design dialog a meaningful name in the title bar labeled Custom Design by default.

Make Table When the Design panel shows the layout you want, click Make Table. This creates the JMP data table whose rows are the runs you defined. Make Table also updates the runs in the Design panel to match the JMP data table. The table to the right is the initial two-factor design shown above, which has four additional center points, and is replicated once as specified above.

initial design

replicate 4 added center points initial design replicate 4 added center points

Chapter 2 Custom Designs

23

Modify a Design Interactively There is a Backup button at several stages in the design dialog that allows you to change your mind and go back to a previous step and modify the design. For example, you can modify the previous design by adding quadratic terms to the model, by removing the center points and the replicate. Figure 2.2 shows the steps to modify a design interactively.

Figure 2.2 Back up to Interactively Modify a Design

2 Customized I

When you click Continue the Design panel shows with 8 runs as default. If you choose the Grid option, the design that results has 9 runs.

24

Chapter 2 Custom Designs

Introducing the Prediction Variance Profiler All of the listed designs in the other design types require at least two factors. The following examples have a single continuous factor and compare designs for quadratic and cubic models. The purpose of these examples is to introduce the prediction variance profile plot.

A Quadratic Model You can follow the steps in Figure 2.3 to create a simple quadratic model with a single continuous factor. 1) Add one continuous factor and click Continue. 2) Select 2nd from the Powers popup menu in the Model panel to create a quadratic term. 3) Use the default number of runs, 6, and click Make Design.

Figure 2.3 Use One Continuous Factor and Create a Quadratic Model

When the design appears, open the Prediction Variance Profile (as shown next). For continuous factors, the initial setting is at the mid-range of the factor values. For categorical factors the initial setting is the first level. If the design model is quadratic, then the prediction variance function is quartic. The three design points are –1, 0, and 1. The prediction variance profile shows that the variance is a maximum at each of these points, on the interval –1 to 1.

Chapter 2 Custom Designs

25

The Y axis is the relative variance of prediction of the expected value of the response.

What you are deciding when you choose a sample size is how much variance in the expected response you are willing to tolerate. As the number of runs increases, the prediction curve (prediction variance) decreases. To compare profile plots, Backup and choose Minimum in the Design Generation panel, which gives a sample size of 3. This produces a curve that has the same shape as the previous plot, but the maxima are at 1 instead of 0.5. Figure 2.4 compares plots for sample size 6 and sample size 3 for this quadratic model example. You can see the prediction variance increase as the sample size decreases.

Figure 2.4 Comparison of Prediction Variance Profiles. These profiles are for middle variance and lowest variance, for sample sizes 6 (top charts) and sample size 3 (bottom charts). .

Note: You can CONTROL-click (COMMAND-click on the Mac) on the factor to set a factor level precisely

2 Customized I

The prediction variance is relative to the error variance. When the prediction variance is 1, the absolute variance is equal to the error variance of the regression model.

26

Chapter 2 Custom Designs

For a final look at the Prediction Variance Profile for the quadratic model, Backup and enter a sample size of 4 in the Design Generation panel and click Make Design. The sample size of 4 adds a point at –1 (Figure 2.5). Therefore, the variance of prediction at –1 is lower (half the value) than the other sample points. The symmetry of the plot is related to the balance of the factor settings. When the design points are balanced, the plot is symmetric, like those in Figure 2.4; when the design is unbalanced, the prediction plot is not symmetric, as shown below. Figure 2.5 Sample Size of Four for the One-Factor Quadratic Model

A Cubic Model The runs in the quadratic model are equally spaced. This is not true for the single-factor cubic model shown in this section. To create a one-factor cubic model, follow the same steps as shown previously in Figure 2.3. In addition, add a cubic term to the model with the Powers popup menu. Use the Default number of runs in the Design Generation panel. Click Make Design to continue. Then open the Prediction Variance Profile Plot to see the Prediction Variance Profile and its associated design shown in Figure 2.6. The cubic model has a variance profile that is a 6th degree polynomial. Note that the points are not equally spaced in X. It is interestingly non-intuitive that this design has a better prediction variance profile than the equally spaced design with the same number of runs.

Chapter 2 Custom Designs

27

You can reproduce the plots in Figure 2.6 with JSL code. The following JSL code shows graphically that the design with unequally spaced points has a better prediction variance than the equally spaced design. Open the file called Cubic Model.jsl, found in the Scripts folder in the Sample Data, and select Submit Script from the Edit menu. When the plot appears, move the free values from the equally spaced points to the optimal points to see that the maximum variance on the interval decreases by more that 10%.

//Start with equally spaced points. u = [-0.333 0.333]; x = {-1,u[1],u[2],1}; y = j(2,1,.2); cubicx = function({x1}, rr=j(4,1,1);for(i=1,i