University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Doctoral Dissertations Graduate School 8-2005 Design, Analysis, and Applications of Failure Amplification Experiments Oksoun Yee University of Tennessee - Knoxville Follow this and additional works at: https://trace.tennessee.edu/utk_graddiss Part of the Business Administration, Management, and Operations Commons Recommended Citation Yee, Oksoun, "Design, Analysis, and Applications of Failure Amplification Experiments. " PhD diss., University of Tennessee, 2005. https://trace.tennessee.edu/utk_graddiss/2310 This Dissertation is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a dissertation written by Oksoun Yee entitled "Design, Analysis, and Applications of Failure Amplification Experiments." I have examined the final electronic copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of the requirements for the degree of Doctor of Philosophy, with a major in Business Administration. Robert W. Mee, Major Professor We have read this dissertation and recommend its acceptance: Mary G. Leitnaker, Ramon V. Leon, Russell L. Zaretzki, Melissa R. Bowers Accepted for the Council: Carolyn R. Hodges Vice Provost and Dean of the Graduate School (Original signatures are on file with official studentecor r ds.) To the Graduate Council: I am submitting herewith a dissertation by Oksoun Yee entitled “Design, Analysis, and Applications of Failure Amplification Experiments.” I have examined the final electronic copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of the requirements for the degree of Doctor of Philosophy, with a major in Business Administration. Robert W. Mee Major Professor We have read this dissertation and recommend its acceptance: Mary G. Leitnaker Ramon V. Leon Russell L. Zaretzki Melissa R. Bowers Accepted for the Council: Anne Mayhew Vice Chancellor and Dean of Graduate Studies (Original signatures are on file with official student records.) DESIGN, ANALYSIS, AND APPLICATIONS OF FAILURE AMPLIFICATION EXPERIMENTS A Dissertation Presented for the Doctor of Philosophy Degree The University of Tennessee, Knoxville Oksoun Yee August 2005 Copyright © 2005 by Oksoun Yee All rights reserved. ii Dedication This dissertation is dedicated to my parents, Yee Sanir and Lim Sunok, for their unending love and support. iii Acknowledgements This work would not have been possible without the support of many people. Many thanks to my advisor, Dr. Robert Mee, for his guidance and support. I feel privileged to have been a student of such a great teacher. I would also like to thank the other members of my dissertation committee. Thanks to Dr. Mary Leitnaker for making it possible for me to work with the Huhtamaki company and for her great advice. I want to thank Dr. Ramon Leon for introducing me to the exciting world of statistical applications in industry through my internships at the General Electric Company and his support. I would also like to thank Dr. Russell Zaretzki and Dr. Melissa Bowers for their help and work as committee members. Thanks to Mark Bond and Mark Pettigrew from the Huhtamaki company for providing me an opportunity of consulting experience and their collaboration. iv Abstract The main focus of this study is related to the Failure Amplification Method (FAMe) proposed by Joseph and Wu (2004). They suggested the use of an “amplification factor” to increase the information from experiments with a binary response variable. In addition to the amplification factor having a known effect, Joseph and Wu recommended that, for convenience of experimentation, this factor be taken as an easy to change, split unit factor. In such cases, the analysis ought to take into account the possibility of both whole unit and split unit error variation. I present such an analysis here, where the Bayesian approach not only permits proper accounting of the error structure, but also facilitates the subsequent optimization step. FAMe can also be extended to categorical data with more than two categories. I helped design an experiment that was conducted at Huhtamaki Consumer Packaging West Inc., Los Angeles, CA, where the response variable was an ordinal variable characterizing the quality of the Tri Web Taco Bell Disk seal. An amplification factor – speed of the production line - was a whole-unit factor that was hard to change. Therefore an application of FAMe to ordinal data is presented here as well. It is crucial to plan an experiment carefully, particularly with categorical responses. Levels of the split-unit factor can be chosen sequentially or set in advance. In the case of the sequential design, a rule for choosing a split-unit factor level will affect consistency and bias of the parameter estimates. Theory-based sequential rules often are impractical in real life situations. Properties of sequential ad hoc designs are studied and compared to fixed designs using complete enumeration and simulation techniques. Key words: Binary Response, Ordinal Response, Generalized Linear Model, Mixed Model, Model Selection, Split Unit, Sequential Design, Optimization. v Table of Contents CHAPTER I........................................................................................................................ 1 Introduction..................................................................................................................... 1 CHAPTER II....................................................................................................................... 4 Analysis of Split Unit Failure Amplification Experiments.............................................. 4 A Brief Overview of Generalized Linear Mixed Models for Binary Data................. 4 Printed Circuit Board Example................................................................................... 6 Paper Feeder Example .............................................................................................. 14 Model Selection with FAME.................................................................................... 18 CHAPTER III ................................................................................................................... 22 Properties of Ad Hoc Sequential Designs with Small Sample Sizes............................. 22 Introduction............................................................................................................... 22 Bias of a Fixed Design with Small Sample Sizes..................................................... 25 Fixed Two-Level Designs with One Factor.............................................................. 26 Comparison of Fixed and Ad Hoc Sequential Rules with Designed Experiments and Small n ...................................................................................................................... 28 CHAPTER IV ................................................................................................................... 33 Composite Disc Experiment.......................................................................................... 33 Introduction............................................................................................................... 33 Design of the Taco Bell Disc Experiment ................................................................ 34 Measurement Process................................................................................................ 35 Analysis of the Continuous Response....................................................................... 38 Categorical Data Analysis......................................................................................... 41 CHAPTER V .................................................................................................................... 47 Conclusions................................................................................................................... 47 LIST OF REFERENCES.................................................................................................. 49 APPENDICES .................................................................................................................. 54 Appendix A: WinBUGS code for PCB data .................................................................. 55 Appendix B: Tables....................................................................................................... 60 Appendix C: Figures..................................................................................................... 98 VITA ..................................................................................................................... 114 vi List of Tables Table 1. Factors and levels for the PCB experiment................................................... 61 Table 2. OA(18, 21 × 37) and data from PCB experiment. ......................................... 62 Table 3. Covariance pattern analysis for opens using GEE........................................ 63 Table 4. Conditional GLMM analysis for opens. ....................................................... 64 Table 5. Bayesian analysis for opens.........................................................................