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Design and Analysis of Accelerated Tests for Mission Critical Reliability - Michael J. LuValle

Design and Analysis of Accelerated Tests for Mission Critical Reliability

Hardcover Published: 27th April 2004
ISBN: 9781584884712
Number Of Pages: 248

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Early approaches to accelerated testing were based on the assumption that there was a simple acceleration factor that would correspond to a linear scaling of time from the operating stress to the accelerating stress. This corresponds to the simplest physical model of the kinetics governing the underlying degradation, but this simple model does not always hold. We need to understand what more complex physical models may look like.

Design & Analysis of Accelerated Tests for Mission Critical Reliability presents innovative theory and methods for recognizing and handling the more complicated, cases often encountered in practice. The theory integrates a physical understanding of underlying phenomena and the statistical modeling of observation "noise" to provide a single theoretical framework for accelerated testing. The treatment includes general approaches that can be used with various computational software packages and an explicit computing environment in S-PLUS. Source code written by the authors is included and available for download from http://www.crcpress.com/e_products/downloads.

For practitioners, this book provides immediately useable tools. For researchers, it presents intriguing open questions. And for the academic community, numerous worked examples, end-of-chapter exercises, and a format that relegates technical and theoretical details to chapter appendices make this an outstanding supplementary textbook for senior and graduate-level students.

Industry Reviews

"I believe that this book could be a good specialized reference text ." - Technometrics, May 2005, Vol. 47, No. 2 "[I]t is a useful and welcome start in an important area. The inclusion of a software system that aids specification and visualization of kinetic models is also welcome. One hopes that this book will spur further research in this area." -Short Book Reviews of the International Statistical Institute "For practitioners, this book provides immediately useable tools. For researchers, it presents intriguing open questions. For the academic community, numerous worked examples, end-of-chapter exercises, and a format that relegates technical and theoretical details to chapter appendices make this an outstanding supplementary textbook for senior and graduate-level students." -Zentralblatt MATH 1053

Backgroundp. 1
Introductionp. 1
Other Approachesp. 2
Foundation of Our Approachp. 5
A Simple Examplep. 6
Organization of This Bookp. 9
Complement: Background Kinetics and Statisticsp. 11
Arrhenius and Relative Humidity Modelsp. 11
First-Order Kineticsp. 14
Binomial Distribution and Its Role in Reliabilityp. 17
Inference for the Binomial Distributionp. 18
Splus Source Code for Matrix Exponentiationp. 20
Demarcation Mapping: Initial Design of Accelerated Testsp. 25
Analytical Theory of Thermal Demarcation Mapsp. 27
Designing an Acceptance Test for a Purely Thermal Processp. 34
Simple Temperature/Humidity Modelsp. 37
Designing an Acceptance Test for a Temperature/Humidity Modelp. 38
Mechanical Cycling Modelsp. 40
Acceptance Testing for Mechanical Cycling Induced by Thermal Cyclingp. 41
Computational Demarcation Mappingp. 44
Beta Binomial Interpretation of 0 Failuresp. 50
An Extrapolation Theoremp. 51
Summaryp. 53
Complements to Chapter 2p. 53
Demarcation Maps for Multiple Experimentsp. 53
Using the Freewarep. 55
Thermal Demarcation Mapsp. 56
Temperature/Humidity Demarcation Mapsp. 58
Mechanical Cycling Demarcation Mapsp. 61
Interface for Building Kinetic Modelsp. 65
Description and Concepts behind the Interfacep. 65
Complement to Chapter 3: Our Interface in Splus, Kinetic Data Objects, and the GUIs to Create Themp. 70
Creating Components of the Kinetic Modelp. 70
Discrete Diffusionp. 71
Creepp. 73
Stress Voidingp. 74
One-Step Processp. 75
One Step with Second Variablep. 77
One Step with Stressp. 77
One Step with Second Variable and Stressp. 78
Glassy One Stepp. 79
Combining Submodelsp. 81
Competing Reactionsp. 81
Mixing Reactionsp. 85
Reversible Reactionsp. 86
Rejoining Reactionsp. 87
Sequential Reactionsp. 89
Simple Connection of Internal Statesp. 90
Computational Demarcation Map Example from Chapter 2p. 92
Evanescent Process Mappingp. 97
Building Blocks for the Theoryp. 98
Model Neighborhoodsp. 98
Risk Orthogonalityp. 102
Model Enumerationp. 102
Integrating the Theoryp. 104
Identifying Neighborhoods of Models, Sampling, and "Chunking"p. 105
Examplep. 111
Summary, Limitations of Accelerated Testingp. 115
Complement to Chapter 4: Using the Evanescent Process Mapping Interface to Duplicate Example 4.3p. 116
Data Analysis for Failure Time Datap. 135
A Simple Data Setp. 136
Adding Physical Sense to the Modelp. 146
Analysis of a Real Data Setp. 148
Summaryp. 158
Complement: Maximum Likelihood Analysisp. 159
Law of Large Numbersp. 160
Central Limit Theoremp. 160
Proof of Consistency of Maximum Likelihoodp. 161
Derivation of the Distribution of the Maximum Likelihood Estimatorp. 162
Splus Source Codep. 164
Complement: Statistical Estimation of Kinetics from Failure Time Datap. 166
Complement: Pseudo-Maximum Likelihood Estimationp. 169
Complement: The Kaplan-Meier Estimatep. 171
Complement: Printed Wiring Board Datap. 171
Complement: Using the Interfacep. 175
Complement: Exercises to Explore Some Questions in Experiment Designp. 190
Problem 5.10.1p. 191
Problem 5.10.2p. 191
Problem 5.10.3p. 191
Hints for Problem 5.10.1p. 191
Hint for Problem 5.10.2p. 196
Hints for Problem 5.10.3p. 196
Data Analysis for Degradation Datap. 197
Motivation and Modelsp. 197
Background for the Examplep. 200
Data Analysis for the Examplep. 201
Complement: Background Statistical Theoryp. 206
Linear Regression and Resultsp. 206
Extension to Nonlinear Regressionp. 208
Extension to an Uncertain Starting Time Modelp. 209
Prediction Uncertainty and Asymptotic Relative Efficiencyp. 212
Complement: Using the Software to Analyze the Example Datap. 213
Complement: Exercises for Data Analysis and Experiment Designp. 224
Referencesp. 227
Installing the Softwarep. 231
Indexp. 233
Table of Contents provided by Rittenhouse. All Rights Reserved.

ISBN: 9781584884712
ISBN-10: 1584884711
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 248
Published: 27th April 2004
Publisher: Taylor & Francis Inc
Country of Publication: US
Dimensions (cm): 23.5 x 15.6  x 1.91
Weight (kg): 0.48
Edition Number: 1

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