RSM Simplified: Optimizing Processes Using Response Surface Methods for Design of Experiments, Second Edition

311 Pages·2016·9.75 MB·English

by  Mark J. Anderson

Second Edition
RSM Simplified
Optimizing Processes Using Response Surface Methods for
Design of Experiments
Second Edition
RSM Simplified
Optimizing Processes Using Response Surface Methods for
Design of Experiments
Mark J. Anderson • Patrick J. Whitcomb
CRC Press
Taylor & Francis Group
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Library of Congress Cataloging-in-Publication Data
Names: Anderson, Mark J., 1953- | Whitcomb, Patrick J., 1950-
Title: RSM simplified : optimizing processes using response surface methods for design of experiments /
Mark J. Anderson and Patrick J. Whitcomb.
Other titles: Response surface methods simplified
Description: Second edition. | Boca Raton : Taylor & Francis, 2016. | “A CRC title.” | Includes
bibliographical references and index.
Identifiers: LCCN 2016003390 | ISBN 9781498745987 (alk. paper)
Subjects: LCSH: Experimental design. | Response surfaces (Statistics)
Classification: LCC QA279 .A52875 2016 | DDC 519.5/7--dc23
LC record available at http://lccn.loc.gov/2016003390
Visit the Taylor & Francis Web site at
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Contents
Preface
Authors
1  Introduction to the Beauty of Response Surface Methods
Strategy of Experimentation: Role for RSM
One Map Better than 1000 Statistics (Apologies to Confucius?)
Using Math Models to Draw a Map That’s Wrong (but Useful!)
Finding the Flats to Achieve Six Sigma Objectives for Robust Design
2
Appendix 1A: Don’t Let R Fool You
2  Lessons to Learn from Happenstance Regression
Dangers of Happenstance Regression
The Storks-Bring-Babies Fallacy, in Which Correlation Implies Causation
Diagnosing Input and Output Data for Outlying and/or Influential Points
Extrapolation Can Be Hazardous to Your Health!
Appendix 2A: A Brief Overview of Matrix Terminology
3  Factorials to Set the Stage for More Glamorous RSM Designs
Putting OFAT in the Fire
Factorial Designs as an Option to OFAT
Two-Level Factorial Design with CPs: A Foundation for RSM
k
A Test for Curvature Tailored to 2 Designs with CPs
Further Discussion on Testing for Lack of Fit (LOF)
The Fork in the Road Has Been Reached!
4  Central Composite Design: Stars Added—RSM Show Begins
Augmenting a Two-Level Factorial with Star Points to Fit Curvature
CCD Example: Part Two of Chemical Reaction Example
How to Select a Good Predictive Model
Inspecting the Selected Model
Model Graphs
Appendix 4A: Details for Sequential Model Sum of Squares Table
Appendix 4B: Details for Lack of Fit Tests
5  Three-Level Designs
The Box–Behnken Design (BBD)
Case Study on Trebuchet
Appendix 5A: Box–Cox Plot for Transformations
6  Finding Your Sweet Spot for Multiple Responses
“Less Filling” versus “Tastes Great!”: Always a Tradeoff
Making Use of the Desirability Function to Evaluate Multiple Responses
Numerical Search for the Optimum
Summary
Case Study with Multiple Responses: Making Microwave Popcorn
Appendix 6A: Simplex Optimization
7  Computer-Generated Optimal Designs
Quantifying Operating Boundaries with Multilinear Constraints
Computer-Generated Design for Constrained Region of Interest
A Real-Life Application for Computer-Generated Optimal Design
Other Applications for Optimal Designs
Appendix 7A: How to Quantify Multilinear Constraints
Appendix 7B: How to Generate a Good Candidate Set
Appendix 7C: An Algorithm for Optimal Point Selection
8  Everything You Should Know about CCDs (but Dare Not Ask!)
Rotatable Central Composite Designs (CCDs)
Going Cuboidal When Your Region of Operability and Interest Coincide
Practical Placement of Stars: Outside the Box but Still in the Galaxy
CPs in Central Composite Designs
Final Comments: How We Recommend That You Construct CCDs
Appendix 8A: Some Details on Blocking CCDs and Issues of Orthogonality
Appendix 8B: Small Composite Designs (SCDs) to Minimize Runs
Good Alternative to SCDs: Minimum-Run Resolution V CCDs
9  RSM for Six Sigma
Developing POE at the Simplest Level of RSM: A One-Factor Experiment
An Application of POE for Three Factors Studied via a BBD
Appendix 9A: Details on How to Calculate POE
POE for Transformed Responses
10  Other Applications for RSM
Adding Categoric Factors to RSM Designs
RSM for Experimenting on Computer Simulations
Appendix 10A: Alternative RSM Designs for Experiments on Simulations
11  Applying RSM to Mixtures
Accounting for Proportional Effects by Creating Ratios of Ingredients
A Different Approach for Optimizing Formulations: Mixture Design
12  Practical Aspects for RSM Success
Split Plots to Handle HTC Factors
Right-Sizing Designs via Fraction of Design Space Plots
How to Confirm Your Models
Glossary
References
Index
About the Software
Preface
Prediction is very hard, especially when it is about the future.
Yogi Berra
This book is a natural progression from our first book, DOE Simplified: Practical Tools
for Effective Experimentation, originally published in 2000 and now in its third edition
(2015). By concentrating on simple comparative and two-level factorial designs, DOE
Simplified provides a topical overview of design of experiments (DOE). Although these
relatively simple statistical tools for breakthrough may require just 20% of the overall
experimental efforts, they likely provide 80% of the gain. From this you can infer that
response surface methods (RSM)—the subject of this book—require the remaining 80%
of effort but net only the final 20% of gain. This may not seem worthwhile, but in
competitive situations in dog-eat-dog high-tech areas, a 20% edge makes all the
difference for success versus failure.
RSM are a paradox in that although the graphical renderings in 3D are readily
grasped by most people, even highly trained technical professionals find it daunting to
get a complete understanding of the underlying principles of experimental design and
mathematical modeling they’re based on. However, the return on investment for
education on RSM can be enormous, particularly for seemingly impossible missions to
meet multiple response specifications on systems affected by a number of key factors.
Delivering RSM in simplified fashion presents a mighty challenge—on par with the
slogan “Statistics Made Easy” that we try to live up to at Stat-Ease, Inc. It’s a very fine
line that Pat and I must walk between oversimplification and unnecessary detail. We
make a good team in this regard in that I, with my education and experience being more
on the business side, tend to gloss over the details and jump to the bottom line, while
Pat happily dives into details on mathematics and statistics. When the two of us hang
together, we form a stable balance as we tread this tightrope—at least we hope so: You,
the reader, must be the judge.
Obviously our publisher would never have agreed to us writing about something as
technical as RSM if the approach we used for DOE Simplified had not proved so
successful. According to the principles of statistical process control (SPC), one should
never tamper with success, so we will carry forward our template—short bursts of
explanatory text and essential formulas, interspersed with sidebars offering amusements
and statistical trivia.
Pat requested that we make RSM Simplified more academic, which I naturally
resisted. However, I quickly realized that with such an advanced topic, it would be
wrong to withhold all the academic details. In RSM Simplified you will see that some of
the sidebars plus the appendices at the end of the chapters offer weightier mathematical
material. These might be big boulders for nonstatistical types attempting to plow
through the book, so we’ve taken them off the main track. If you’re like me, you won’t
sweat these details, but those of you who, like Pat, thrive on math, will want to pore
over every equation and perhaps work them out for yourselves. Knock yourself out!
Along these lines, another departure from the format of DOE Simplified will be more
liberal referencing to documents offering greater detail on technical material. Again, we
hope to serve both types of readers, the experimenters who lack formal statistical
education and the statisticians who must advise experimenters.
As we stated at the outset, RSM Simplified rests on the foundation we built with its
predecessor—DOE Simplified. Therefore, to minimize redundancy, we must assume
that you have achieved proficiency in the basics of design and analysis of experiments.
In other words, DOE Simplified or its equivalent is a prerequisite for RSM Simplified.
You will see numerous cross-references to DOE Simplified throughout this book in lieu
of a rehash of material we’ve previously detailed.
A big factor in the success of DOE Simplified was its “hands-on” approach facilitated
by inclusion of software tailored to the techniques taught in the book. It would be
inconceivable in the twenty-first century to pursue RSM without the use of computers.
We’ve made this very easy by providing as a companion to the book an advanced
program with all the necessary tools to do RSM. Practice problems are provided at the
end of each chapter, with directions on how to make use of the computational tools. If
you’re serious about gaining a working knowledge of RSM, we urge you to download
the software, which is a fully functional, but time-limited educational version of a
commercially available package. You will find details on how to do this in the “About
the Software” page at the end of the book. There you are provided a path to a website
offering the software download, plus files associated with the book. Throughout the
book you will be directed to software tutorials that facilitate completion of practice
problems. Even if you ultimately make use of different statistical software, you will
round out your education on RSM by working through all the suggested tutorials. Also,
try reproducing other cases cited in the text by opening and analyzing data files
provided at the book’s website. There you will also find solutions to problems not
already detailed via software tutorials. A final heads-up: Check out the on-line help
incorporated with the software—it offers a wealth of knowledge, not just about program
features, but about the statistics themselves.
As we’ve discussed, RSM Simplified goes into a lot more detail than its predecessor
—DOE Simplified. However, this time around we decided not to include all of the
dozens of design templates developed for RSM. We can cover only the proverbial tip of
the iceberg in the text. Within each major class of design, RSM Simplified provides at
least one detailed design template, plus one or two practice problems. Beyond that, you
must make use of the software to view a complete catalog of templates, or you can
follow up on the references to original statistical articles specifying their construction.