Design and Analysis of Experiments by Douglas Montgomery. Heath Rushing

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      About These Authors

       Heath Rushing, Principal Consultant and co-founder of Adsurgo, LLC, an analytics consulting company that specializes in commercial and government training. Heath is a former professor from the Air Force Academy. He holds an M.S. degree in Operations Research from the Air Force Institute of Technology and has used JMP since 2001. After teaching at the Academy, Heath was a quality engineer and Six Sigma Black Belt in both biopharmaceutical manufacturing and Research and Development, where he used JMP to design and deliver training material in Six Sigma, Statistical Process Control (SPC), Design of Experiments (DOE), and Measurement Systems Analysis (MSA). In addition, Heath has been a symposium speaker at both national and international pharma and medical device conferences. Heath is an American Society of Quality (ASQ) Certified Quality Engineer and teaches JMP courses regularly, including a course he recently developed on Quality by Design (QbD) using JMP.

       Andrew T. Karl is a senior management consultant for Adsurgo, LLC, developing and teaching courses on a variety of statistical topics for the U.S. Department of Defense, Fortune 500 corporations, and international clients. He received his B.A. in mathematics from the University of Notre Dame and his Ph.D. in statistics from Arizona State University. Dr. Karl’s research interests focus on computation and applications of non-nested linear and nonlinear mixed models, including value-added problems. Additionally, he frequently works with problems from data mining, text mining, and experimental design.

       Jim Wisnowski is co-founder and principal at Adsurgo, LLC, an analytics consulting company that specializes in commercial and government training. He has a Ph.D. in Industrial Engineering from Arizona State University and has published numerous journal articles and textbook chapters. He was an award-winning professor and statistics chair while at the United States Air Force Academy. Jim retired from the Air Force, where he held various analytical and leadership positions throughout the Department of Defense in training, test and evaluation, human resources, logistics, systems engineering, and acquisition.

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      Acknowledgments

      All three authors have been students of Dr. Douglas Montgomery; two literally, one figuratively. We could not have even considered writing this book without the experiences of having studied under Dr. Montgomery, and both taking and teaching courses using multiple versions of his text. It is generally regarded as the most useful text for design of experiments; we understand why.

      We would like to acknowledge the contributions of those who helped us write this supplement. Thanks to the several technical reviewers at SAS who took the time to carefully review the draft: Mark Bailey, Mia Stephens, Paul Marovich, and Di Michelson. Also, thanks to Dr. Jianbiao John Pan from California Polytechnic State University San Luis Obispo who provided comments and suggestions for the supplement. We would be remiss if we did not acknowledge the contributions of the JMP software development team, specifically Bradley Jones and Chris Gotwalt, who continually improve the software and listen to customer input.

      Thank you to Shelley Sessoms, the SAS Press Acquisitions Editor, who provided us with this opportunity. Thanks to the SAS Publications Editing and Production staff for making corrections and improvements to the book: Kathy Underwood, Candy Farrell, Thais Fox, Robert Harris, Stacy Suggs, and Denise Jones. Finally, a special thanks to SAS Press Developmental Editor John West and SAS Publications Marketing Specialist Cindy Puryear for managing this project and keeping us on track.

      1

      Introduction

      The analysis of a complex process requires the identification of target quality attributes that characterize the output of the process and of factors that may be related to those attributes. Once a list of potential factors is identified from subject-matter expertise, the strengths of the associations between those factors and the target attributes need to be quantified. A naïve, one-factor-at-a-time analysis would require many more trials than necessary. Additionally, it would not yield information about whether the relationship between a factor and the target depends on the values of other factors (commonly referred to as interaction effects between factors). As demonstrated in Douglas Montgomery’s Design and Analysis of Experiments textbook, principles of statistical theory, linear algebra, and analysis guide the development of efficient experimental designs for factor settings. Once a subset of important factors has been isolated, subsequent experimentation can determine the settings of those factors that will optimize the target quality attributes. Fortunately, modern software has taken advantage of the advanced theory. This software now facilitates the development of good design and makes solid analysis more accessible to those with a minimal statistical background.

      Designing experiments with specialized design of experiments (DOE) software is more efficient, complete, insightful, and less error-prone than producing the same design by hand with tables. In addition, it provides the ability to generate algorithmic designs (according to one of several possible optimality criteria) that are frequently required to accommodate constraints commonly encountered in practice. Once an experiment has been designed and executed, the analysis of the results should respect the assumptions made during the design process. For example, split-plot experiments with hard-to-change factors should be analyzed