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Iqbal's ideas on Science and the Muslims

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  • leçon - matière potentielle : rumi‟s mathnawi
  • dissertation
  • exposé
  • expression écrite
1 Iqbal's ideas on Science and the Muslims (Dr. Mohd Abbas Abdul Razak) Department of General Studies Kulliyyah of Islamic Revealed Knowledge and Human Sciences International Islamic University Malaysia Muslims were able to embellish their civilization with great achievements in the areas of science and technology. The Holy Qur‟an not only speaks about spirituality but also on science and the natural world. The message found in the Qur‟an was the driving force in encouraging the Muslims to go into science and research.
  • spiritual practices
  • religious point of view
  • muslim scholars
  • ego philosophy
  • iqbal‟s
  • realization of the power of the human ego
  • philosophy
  • islam
  • life
  • muslims

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OPTIMAL EXPERIMENTAL DESIGNS FOR ACCELERATED LIFE TESTS WITH

CENSORING AND CONSTRAINTS

by

Eric Michael Monroe



















A Dissertation Presented in Partial Fulfillment
of the Requirements for the Degree
Doctor of Philosophy



















ARIZONA STATE UNIVERSITY

May 2009
















































©2009 Eric Michael Monroe
All Rights Reserved OPTIMAL EXPERIMENTAL DESIGNS FOR ACCELERATED LIFE TESTS WITH

CENSORING AND CONSTRAINTS

by

Eric Michael Monroe




has been approved

April 2009














Graduate Supervisory Committee:

Rong Pan, Co-Chair
Douglas C. Montgomery, Co-Chair
Christine M. Anderson-Cook
Connie M. Borror
Robert L. Parker














ACCEPTED BY THE GRADUATE COLLEGE ABSTRACT
Manufacturers are continually faced with customer expectations to deliver products
faster while assuring high reliability. Companies must diligently plan and execute acceler-
ated life tests in order to insure future reliability performance is met. In many industrial
applications, accelerated life test results involve considerations that hinder the ability of the
analyst to easily de ne a suitable test plan. A methodology for de ning e cient, yet discern-
ing, tests could insure that corporate investments in reliability testing are properly selected
to mitigate risk while minimizing cost. This dissertation consists of three main studies.
First, classical design of experiment methods are extended to multi-stress accelerated life
test plans. This investigation mitigates the uncertainty in model parameter estimation for
non-linear models with censoring and constrained feasible design regions. An electronics
industry case study serves as the motivation for this research. Inference comparisons are
drawn against current best practices documented in the literature. Second, an alternate
technique for determining an optimal stress test level is introduced using a generalized linear
model framework. This approach achieves equivalent results to traditional maximum likeli-
hood estimation techniques, but avoids the necessity to compute complex rst and second
partial derivatives. In addition, it avoids the convergence problems associated with locally
optimal solutions. Finally, a sensitivity and robustness study demonstrates additional tools
to use in the planning of accelerated life tests.
iiiTo Janelle and Jackson.
ivACKNOWLEDGMENTS
The writing of a dissertation is a highly individualized and internally-focused en-
deavor, yet it is not possible without the personal and professional support of numerous
people. Thus, my sincere gratitude goes to faculty, fellow colleagues, friends, and family
for their time, support, and patience over the years. Without their help, this dissertation
would not have been possible.
I especially want to thank Dr. Douglas C. Montgomery and Dr. Rong Pan for being
the co-chairs of my Ph.D. committee. I wish to thank Dr. Montgomery, who assisted me
in entering the Ph.D. program and provided me guidance both as a student and as a full-
time working professional. To Dr. Pan, I appreciate his countless hours of mentoring and
coaching during the writing process. I also would like to thank my committee members, Dr.
Christine M. Anderson-Cook, Dr. Connie M. Borror, and Dr. Robert L. Parker for timely
advice at critical points along the way. Also, I would like to thank the National Science
Foundation for their support of my research through research grant CMMI-0654417.
My graduate study would not have been the same without the social, professional,
and academic support I have received. I am particularly thankful for the support of my
friend, Jinsuk Lee, in learning the Latex syntax used to format my dissertation. Profession-
ally, I would like to thank Intel Corporation for their nancial and temporal support. In
particular, I’d like to thank my supervisors that o ered me the exibility to manage both
an academic and professional career. They are Kenneth T. Yee, Nicholas P. Mencinger,
Mary A. VerHelst, Derek M. Wolfe, and Eric R. Gee. Academically, I would like to express
my gratitude to the faculty and sta of the Industrial Engineering department at Arizona
State University for their assistance and encouragement during my course of study.
vFinally, I wish to acknowledge all of my friends and family. They have listened to
me moan, cheer, complain, laugh, and ponder my way through this academic program over
the years, but also provided me with emotional support throughout this long process. I
wish to especially thank my wife, Janelle, who provided never-ending support and endured
many of my late night working sessions. This endeavor would not have succeeded without
their fullest support.
viTABLE OF CONTENTS
Page
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
CHAPTER 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3. Research objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
4. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
CHAPTER 2 LITERATURE REVIEW . . . . . . . . . . . . . . . . . . . . . . . . 7
1. Accelerated life testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2. Optimal experimental designs . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1. Historical overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2. Relevant literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3. Alphabetic optimality criteria . . . . . . . . . . . . . . . . . . . . . . 12
2.4. Computer algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.1. Point exchange algorithms . . . . . . . . . . . . . . . . . . 16
2.4.2. Branch-and-bound methods . . . . . . . . . . . . . . . . . . 18
2.4.3. Simulated annealing . . . . . . . . . . . . . . . . . . . . . . 18
2.4.4. Coordinate-exchange algorithms . . . . . . . . . . . . . . . 19
2.4.5. Genetic algorithms . . . . . . . . . . . . . . . . . . . . . . . 21
2.5. Software integration . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.6. Applications in reliability . . . . . . . . . . . . . . . . . . . . . . . . 24
3. Unknown model parameter dependency . . . . . . . . . . . . . . . . . . . . 25
viiPage
3.1. Parameter dependency . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2. Model-robust designs . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3. Model-sensitive designs . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4. Bayesian designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.5. Multifaceted selection criteria designs . . . . . . . . . . . . . . . . . 30
4. Use of a Bayesian D-optimal criterion in designing accelerated life tests . . 31
5. Generalized Linear Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
CHAPTER 3 OPTIMAL DESIGNS FOR CONSTRAINED REGIONS . . . . . . 35
1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2. Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3. Data collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.1. Acceleration model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2. Irregular feasible design region . . . . . . . . . . . . . . . . . . . . . 40
3.3. Legacy experiments and preliminary data analysis . . . . . . . . . . 42
4. Analysis and interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.1. Experimental designs and simulation study . . . . . . . . . . . . . . 45
4.2. E ects of experimental design, sample size, and censoring . . . . . . 48
4.3. Alternative test plan with Type-I censoring . . . . . . . . . . . . . . 50
5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
6. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
CHAPTER 4 A GLM APPROACH TO DESIGNING ACCELERATED LIFE TESTS 55
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
1.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
viiiPage
1.2. Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
1.3. Scope of work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2. Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.1. Maximum likelihood estimation approach . . . . . . . . . . . . . . . 60
2.2. Generalized linear model approach to failure time analysis . . . . . . 62
3. Computational procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.1. Search methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.2. Initial values and convergence criteria . . . . . . . . . . . . . . . . . 68
4. Numerical examples and results . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.1. Case study 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.2. Case study 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
CHAPTER 5 SENSITIVITY AND ROBUSTNESS ANALYSIS . . . . . . . . . . 83
1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
2. Numerical example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3. In uence of parameter uncertainty on U-optimal design performance . . . . 86
3.1. Uncertainty range . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.2. Design construction sensitivity . . . . . . . . . . . . . . . . . . . . . 90
3.3. Prediction variance sensitivity for a single acceleration factor . . . . 91
3.4. Prediction variance sensitivity for multiple factors . . . 93
4. Mitigation schemes using controllable design factors . . . . . . . . . . . . . 97
5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
CHAPTER 6 CONCLUSIONS AND FUTURE WORK . . . . . . . . . . . . . . . 100
ix