Reliability Modeling, Prediction, and Optimization

by Blischke, Wallace R.; Murthy, D. N. Prabhakar

• ISBN13: 9780471184508
• ISBN10: 0471184500
• Edition: 1st
• Format: Hardcover
• Copyright: 2000-03-27
• Publisher: Wiley

Summary

Bringing together business and engineering to reliability analysis With manufactured products exploding in numbers and complexity, reliability studies play an increasingly critical role throughout a product's entire life cycle-from design to post-sale support. Reliability: Modeling, Prediction, and Optimization presents a remarkably broad framework for the analysis of the technical and commercial aspects of product reliability, integrating concepts and methodologies from such diverse areas as engineering, materials science, statistics, probability, operations research, and management. Written in plain language by two highly respected experts in the field, this practical work provides engineers, operations managers, and applied statisticians with both qualitative and quantitative tools for solving a variety of complex, real-world reliability problems. A wealth of examples and case studies accompanies: 'ˆ— Comprehensive coverage of assessment, prediction, and improvement at each stage of a product's life cycle 'ˆ— Clear explanations of modeling and analysis for hardware ranging from a single part to whole systems 'ˆ— Thorough coverage of test design and statistical analysis of reliability data 'ˆ— A special chapter on software reliability 'ˆ— Coverage of effective management of reliability, product support, testing, pricing, and related topics 'ˆ— Lists of sources for technical information, data, and computer programs 'ˆ— Hundreds of graphs, charts, and tables, as well as over 500 references 'ˆ— PowerPoint slides are available from the Wiley editorial department.

Author Biography

WALLACE R. BLISCHKE, PhD, Statistics, is Professor Emeritus, Marshall School of Business, University of Southern California.<br> <br> PRABHAKAR MURTHY, PhD, is Professor of Engineering and Operations Management at the University of Queensland, St. Lucia, Australia.

Table of Contents

PART A: CONTEXT OF RELIABILITY ANALYSIS
An Overview	3	(28)
Introduction	3	(1)
Illustrative Examples of Products and Systems	4	(8)
Incandescent Electric Bulb	6	(1)
Hydraulically Operated Fail-Safe Gate Valve	6	(1)
Pneumatic Pump	7	(1)
Brake Mechanism for Train Wagons	8	(1)
Liquid Rocket Engine	8	(4)
Electric Power System	12	(1)
System and Product Deterioration and Failure	12	(6)
Failures and Faults	13	(2)
Failure Modes	15	(1)
Failure Causes and Severity	16	(1)
Deterioration	17	(1)
Concepts and History of Reliability	18	(1)
Basic Concepts	18	(1)
A Brief History of Reliability	19	(1)
Product Life Cycle and Reliability	19	(2)
Buyer's Perspective	21	(2)
Individuals	22	(1)
Businesses	22	(1)
Government	22	(1)
Manufacturer's Perspective	23	(1)
Framework for Solving Reliability Related Problems	24	(3)
Reliability Issues	24	(1)
The Systems Approach	25	(2)
Objectives of this Book	27	(1)
Approach	27	(1)
Outline of this Book	27	(4)
Notes	28	(1)
Exercises	29	(2)
Illustrative Cases and Data Sets	31	(36)
Introduction	31	(1)
Reliability Data	32	(1)
Cases	33	(34)
Reliability of a Simple Part	33	(2)
Reliability of a Major Component (Incomplete Data)	35	(2)
Heart Pacemaker Data	37	(1)
Automobile Warranty Data	38	(1)
Industrial Product Sold in Batches	39	(2)
Tensile Strength of Fibers	41	(2)
Reliability of Hydraulic Systems	43	(1)
Bus Motor Failure Data	44	(1)
Lifetimes of Light Bulbs	45	(1)
Air Conditioning Unit Failures	45	(1)
Electronic Connectors	45	(1)
Laser Weld Strength	45	(2)
Clerical Errors	47	(2)
Ball Bearing Data	49	(2)
Helicopter Failure Data	51	(1)
Compressor Failure Data	51	(3)
Jet Engines	54	(1)
Offshore Oil Exploration Equipment	54	(1)
Throttle Failures	55	(1)
Breaking Strengths of Single and Bundled Fibers	56	(1)
Breaking Strengths of Carbon Fibers in Resin	56	(1)
Stress Fatigue Failures, Tungsten Alloy	56	(1)
Software Reliability	56	(4)
Aircraft Radar Component Failures	60	(1)
Ship Engine Maintenance	60	(1)
Failures of Electronic Modules	61	(2)
Nuclear Power Plant Cooling System	63	(1)
Notes	63	(1)
Exercises	64	(3)
PART B: BASIC RELIABILITY METHODOLOGY
Collection and Preliminary Analysis of Failure Data	67	(26)
Introduction	67	(1)
Data-Based Reliability Analysis	68	(4)
Levels of Data	68	(1)
Types of Data and Data Sources	69	(2)
Use of Data in Reliability Analysis	71	(1)
Attribute Data	72	(2)
Data Structure	72	(1)
Count Data	73	(1)
Test Data on Product Lifetimes (Failure Data)	74	(2)
Complete and Incomplete Data	74	(1)
Types of Censoring	75	(1)
Effect of Data Structure on Statistical Analysis	76	(3)
Scales of Measurement	77	(1)
Statistical Inference	78	(1)
Basic Descriptive Statistics	79	(10)
Frequency Distributions	79	(3)
Other Graphical Methods	82	(4)
Measures of Center	86	(1)
Measures of Variability	87	(1)
Interpretation of the Mean and Standard Deviation	88	(1)
Other Data Characteristics	88	(1)
Preliminary Analysis of Reliability Data	89	(4)
Description and Summarization of Pass/Fail Data	89	(1)
Description and Summarization of Complete Failure Data	89	(1)
Description and Summarization of Incomplete Failure Data	89	(1)
Notes	90	(1)
Exercises	90	(3)
Probability Distributions for Modeling Time to Failure	93	(42)
Introduction	93	(1)
Random Variables and Probability Distributions	94	(4)
Random Variables	94	(1)
Distribution and Density Functions	95	(1)
Failure Distributions	96	(1)
Moments	97	(1)
Fractiles and Median	98	(1)
Basic Discrete Distributions	98	(5)
Bernoulli Distribution	98	(1)
Binomial Distribution	99	(1)
Geometric Distribution	100	(1)
Negative Binomial Distribution	100	(1)
Hypergeometric Distribution	101	(1)
Poisson Distribution	102	(1)
Continuous Distributions---I (Basic Distributions)	103	(8)
Exponential Distribution	103	(1)
Gamma Distribution	104	(2)
Weibull Distribution	106	(2)
Normal (Gaussian) Distribution	108	(1)
Inverse Gaussian Distribution	109	(1)
Gumbel Distributions	110	(1)
Continuous Distributions---II (Derived Distributions)	111	(4)
Lognormal Distribution (Category A)	111	(2)
Three Parameter Weibull Distribution (Category B)	113	(1)
Truncated Gumbel Distribution of the Smallest Extreme	113	(1)
Distribution Derived from Gumbel Distribution of the Largest Extreme (Category A)	113	(1)
Exponentiated Weibull Distribution (Category B)	114	(1)
Continuous Distributions---III (Involving Several Basic Distributions)	115	(4)
Mixtures of Distributions	115	(1)
Competing Risk Models	116	(1)
Multplicative Models	116	(1)
Sectional Models	117	(1)
Special Case: K = 2 and Weibull Distributions	117	(2)
Classification of Failure Distributions	119	(5)
Definitions and Classification	120	(2)
Bounds on Reliability	122	(2)
Shapes of Density Functions	124	(1)
Shapes of Failure-Rate Functions	125	(4)
Failure-Rate Classification	125	(3)
Bathtub Failure Rate	128	(1)
Effect of Environmental Factors	129	(1)
Conclusions	130	(5)
Notes	130	(1)
Exercises	131	(4)
Basic Statistical Methods for Data Analysis	135	(34)
Introduction	135	(1)
Estimation	136	(12)
Overview	136	(1)
Properties of Estimators	137	(2)
Moment Estimators	139	(4)
Maximum Likelihood Estimators	143	(5)
Confidence Interval Estimation	148	(5)
Basic Concepts	148	(2)
Confidence Intervals for the Parameters of Distributions Used in Reliability	150	(3)
Estimation of Functions of Parameters	153	(2)
Basic Approach	153	(1)
Functions of Random Variables	154	(1)
Tolerance Intervals	155	(2)
Basic Concept	155	(1)
Normal Tolerance Limits	155	(1)
Tolerance Intervals for the Exponential Distribution	156	(1)
Nonparametric Tolerance Intervals	156	(1)
Hypothesis Testing	157	(12)
Basic Concepts	157	(2)
Testing Hypotheses About the Mean of a Normal Distribution	159	(2)
Relationship Between Hypothesis Testing and Confidence Interval Estimation	161	(1)
Suggested Approach to Testing Hypotheses	161	(1)
Notes	162	(1)
Exercises	162	(7)
PART C: RELIABILITY MODELING, ESTIMATION, AND PREDICTION
Modeling Failures at the Component Level	169	(32)
Introduction	169	(1)
Modeling Failure Mechanisms	170	(1)
Overstress Failure Mechanisms	171	(2)
Large Elastic Deformation	172	(1)
Yield	172	(1)
Buckling	173	(1)
Brittle Fracture	173	(1)
Ductile Fracture	173	(1)
Interfacial De-Adhesion	173	(1)
Wearout Failure Mechanisms	173	(2)
Fatigue Crack Initiation and Growth	173	(1)
Diffusion and Interdiffusion	174	(1)
Creep	174	(1)
Corrosion and Stress Corrosion Cracking	174	(1)
Wear	175	(1)
Other Mechanisms	175	(1)
Static Reliability: Stress---Strength Models	175	(2)
Deterministic Stress and Random Strength	176	(1)
Random Stress and Strength	176	(1)
Modeling Failure Based on the Failure Mechanism	177	(9)
Overstress Failure Modeling	178	(3)
Wear-out Failure Modeling	181	(3)
Wear-out Modeling with Sudden Failure	184	(1)
Some Other Models	185	(1)
Multistate Models	186	(1)
Modeling Failures of Repaired Items	187	(3)
Types of Repair	187	(2)
Total Repair Time	189	(1)
Repair Cost	190	(1)
Modeling Failures over Time	190	(4)
Nonrepairable Items	190	(2)
Repairable Items	192	(2)
Modeling Environmental Effect	194	(4)
Arrhenius Life-Temperature Relationship	194	(2)
Inverse Power Law	196	(1)
Other Relationships	196	(1)
Proportional Hazard Models	197	(1)
Modeling Failures of Intermittently Used Items	198	(3)
Notes	198	(1)
Exercises	199	(2)
Modeling and Analysis of Multicomponent Systems	201	(42)
Introduction	201	(1)
System Characterization and Failures	202	(3)
System Characterization	202	(2)
System Failures	204	(1)
Black-Box Modeling	205	(1)
White-Box Modeling	206	(1)
Failure Mode, Effects, and Criticality Analysis	207	(2)
Fault Tree Analysis	209	(11)
Definition of the TOP Event	210	(1)
Fault Tree Construction	210	(4)
Qualitative Analysis	214	(5)
Comparison with FMECA	219	(1)
Reliability Block Diagram Representations and Analysis	220	(8)
Link to Fault Tree Representation	221	(1)
Structure Functions	222	(2)
Coherent Systems	224	(1)
Path and Cut Sets	224	(2)
System Reliability	226	(2)
Reliability and Structural Importance of a Component	228	(2)
Structural Importance of Components	228	(1)
Reliability Importance of Components	229	(1)
Markovian Model Formulations	230	(5)
Basic Concepts	230	(1)
Special Case (n = 2)	230	(5)
General Case	235	(1)
Dependent Failures	235	(4)
Multivariate Distribution Models	235	(2)
Shock Damage Model	237	(1)
Common Environment Model	237	(1)
Other Models	238	(1)
Other Issues	239	(1)
Failure Interaction Models	239	(4)
Notes	239	(1)
Exercises	240	(3)
Advanced Statistical Methods for Data Analysis	243	(44)
Introduction	243	(1)
Analysis of Grouped Data	244	(1)
Estimating the Mean and Variance Using Grouped Data	244	(1)
Maximum Likelihood Estimation Using Grouped Data	245	(1)
Analysis of Censored Data	245
Basic Concepts	246	(1)
Inference for Censored Data	246	(1)
Application to Selected Failure Distributions	247	(7)
Related Analyses and Results	254
Bayesian Statistical Analysis	2543B	(262)
Concept and Basic Approach	255	(3)
Bayes Estimation for Selected Distributions	258	(2)
Bayesian Probability Intervals	260	(2)
Use of Aggregated Data in Reliability Analysis	262	(3)
Data Sources	262	(1)
Formulation of Prior Distributions	263	(2)
Estimation of System Reliability	265	(11)
System Models	265	(1)
Inferences Based on Life Test Data	265	(4)
Estimation of System Reliability from Component Reliabilities	269	(4)
Bayesian Analysis of MultiComponent Systems	273	(3)
Other Inference Problems in Reliability	276	(11)
Estimation in Stress-Strength Analysis	276	(2)
Comparison of Parameters	278	(1)
Estimation of Parameters of Intensity Functions	279	(2)
Notes	281	(2)
Exercises	283	(4)
Software Reliability	287	(32)
Introduction	287	(2)
The Need for Reliable Software	287	(2)
Chapter Outline	289	(1)
Software Quality and Reliability Issues	289	(7)
Definitions	289	(1)
Types and Severity of Errors in Software	290	(3)
Hardware Versus Software Reliability	293	(1)
Dimensions of Software Quality	294	(1)
Software Quality and Reliability Standards	295	(1)
Design of Reliable Software	296	(3)
Software Life Cycle	296	(1)
Software Reliability Requirements and Specifications	297	(1)
Software Reliability Engineering	297	(2)
Software Quality Assurance	299	(1)
Modeling and Measurement of Software Reliability	299	(11)
Metrics and Data	299	(2)
Software Reliability Models	301	(6)
Estimation of Model Parameters and Software Reliability	307	(3)
Estimation of the Number of Remaining Defects	310	(1)
Software Testing Procedures	310	(5)
Basic Principles of Software Testing	311	(1)
Testing Methodology	312	(2)
Tools for Testing Software	314	(1)
Management of Software Reliability	315	(4)
Exercises	317	(2)
Design of Experiments and Analysis of Variance	319	(56)
Introduction	319	(2)
Basic Concepts of Experimentation	321	(4)
Experimentation and the Scientific Method	321	(1)
Definitions	322	(1)
Randomization	323	(1)
Replication	323	(1)
Mathematical Models in DOE	324	(1)
Approach to Designing an Experiment	324	(1)
Some Basic Experimental Designs	325	(9)
The Completely Randomized Design	325	(1)
Randomized Block and Latin Square Designs	326	(1)
Factorial Experiments	327	(4)
Other Experimental Designs	331	(3)
Analysis of Variance I. The Completely Randomized Design	334	(11)
Objectives, Models, and Assumptions of ANOVA	334	(1)
ANOVA for the CRD, Test Statistics and Interpretation	335	(4)
Confidence Intervals	339	(1)
Multiple Comparisons	340	(4)
Tests of Assumptions	344	(1)
Analysis of Variance II. Factorial Experiments	345	(4)
The Completely Randomized Design	345	(3)
Other Experimental Designs	348	(1)
Analysis of Variance III. Complete Block Designs	349	(4)
ANOVA for the Randomized Complete Block Design	349	(1)
ANOVA for the Latin Square Design	350	(1)
ANOVA for the Split-Plot Design	351	(2)
Analysis of Variance IV. BIBD and Fractional Factorial Designs	353	(5)
Balanced Incomplete Block Designs	353	(1)
Fractional Factorial Designs	354	(3)
Taguchi Designs	357	(1)
Regression, Correlation, and Covariance Analysis	358	(11)
Introduction	358	(1)
The Linear Regression Model and Assumptions	358	(3)
Inferences in Linear Regression	361	(6)
Linear Correlation	367	(1)
Analysis of Covariance	368	(1)
Accelerated Test Designs	369	(6)
Notes	370	(1)
Exercises	370	(5)
Model Selection and Validation	375	(52)
Introduction	375	(2)
Graphical Methods	377	(19)
Plotting the Sample CDF	377	(1)
Probability Plots, Complete Data	378	(4)
Hazard Plots, Complete Data	382	(5)
Graphical Estimation of Parameters	387	(6)
Plots for Censored Data	393	(3)
Goodness-of-Fit Tests	396	(10)
Basic Concepts	396	(1)
Fitting Discrete Distributions: The Chi-Square Test	397	(2)
Fitting Continuous Distributions, General Approaches	399	(2)
Fitting Specific Continuous Distributions, Parameters Unknown	401	(5)
Model Selection	406	(10)
Selection of a Life Distribution	406	(7)
Reliability Models	413	(1)
Interpretation of Lack of Fit: Alternative Models	413	(1)
Sensitivity Studies	414	(2)
Model Validation	416	(11)
Criteria for Validation	416	(2)
Data-Based Model Validation	418	(2)
Notes	420	(1)
Exercises	421	(6)
PART D: RELIABILITY MANAGEMENT, IMPROVEMENT, AND OPTIMIZATION
Reliability Management	427	(40)
Introduction	427	(1)
Product Life Cycle	428	(2)
Manufacturer's and Buyer's Points of View	429	(1)
Product Life Cycle for Reliability Management	430	(1)
Strategic Management	430	(3)
Basic Concepts	430	(2)
Planning and Implementation	432	(1)
Comment	433	(1)
Reliability and Quality	433	(2)
Total Quality Management (TQM)	435	(2)
The TQM Concept	435	(1)
Customer Satisfaction	436	(1)
Strategic Reliability Management (Manufacturer's Perspective)	437	(4)
Customer Durables and Commercial and Industrial Products	437	(4)
Specialized Defense Products	441	(1)
Strategic Reliability Management (Buyer's Perspective)	441	(3)
Commercial and Industrial Products	442	(2)
Defense Products	444	(1)
Reliability Programs	444	(8)
MIL-STD 785	444	(1)
Other Defense Standards	445	(1)
ISO Standards	446	(1)
British Standards	446	(1)
IEC Standards	446	(2)
SAE M-100	448	(1)
Norwegian Petroleum Industry	448	(2)
Other Standards for Commercial Products	450	(1)
Some Other Issues	451	(1)
Reliability, Risk and Liability	452	(1)
New Product Risk	452	(1)
Product Liability	452	(1)
Customer Assurance	453	(2)
Realiability Contract	453	(1)
Warranties	454	(1)
An Illustrative Example of an Integrated Model	455	(2)
Quantitative Approach to Reliability Management	457	(3)
Software Issues	460	(2)
Basic Concepts	460	(1)
Completeness	461	(1)
Design for Safety	461	(1)
Tools to Improve Safety	462	(1)
Software Maintainability	462	(1)
Basic Concepts	462	(1)
Design Issues	463	(1)
Concluding Comments	463	(4)
Notes	463	(1)
Exercises	463	(4)
Reliability Engineering	467	(44)
Introduction	467	(1)
The Engineering Process	468	(2)
The Reliability Process	469	(1)
Reliability Engineer and Associated Tasks	470	(1)
Design for Reliability (DFR)	470	(3)
Design and Development	473	(12)
Requirement Definition	473	(5)
Conceptual Design	478	(1)
Detailed Design and Development	479	(5)
Key Design Practices	484	(1)
Reliability Allocation and Apportionment	485	(3)
Approaches to Reliability Allocation	485	(3)
Optimal Reliability Allocation	488	(1)
Designing at the Component Level	488	(4)
Designing for Static Reliability	489	(2)
Designing for Dynamic Reliability	491	(1)
Manufacturing and Reliability Degradation	492	(7)
Reliability Characterization on Nonconforming Items	493	(2)
Modeling Occurrence on Nonconforming Items	495	(4)
Control of Reliability Degradation	499	(3)
Weeding Out Nonconforming Items	499	(1)
Prevention of the Occurrence of Nonconforming Items	500	(2)
Process Improvement	502	(1)
Testing	502	(2)
Development Testing	502	(1)
Testing During Manufacturing	503	(1)
Operational Testing	504	(1)
Testability	504	(1)
Burn-in	504	(7)
Weeding Out Nonconforming Items	504	(1)
Presale Testing	505	(2)
Notes	507	(1)
Exercises	508	(3)
Reliability Prediction and Assessment	511	(26)
Introduction	511	(1)
Context of Product Reliability Prediction and Assessment	512	(5)
Product Life Cycle	512	(1)
Illustrative Cases of Products and Systems	513	(3)
Target values for reliability	516	(1)
Reliability Evaluation over the Product Life Cycle	516	(1)
Reliability Prediction	517	(8)
Importance of Reliability Prediction	517	(1)
Prediction at the Conceptual Stage of Design	518	(1)
Tools for Failure Analysis	518	(2)
Methods of Reliability Prediction	520	(2)
Environmental Factors	522	(2)
Prediction at Later Stages	524	(1)
The Role of Testing	525	(1)
Accelerated Tests	526	(5)
Design of Accelerated Tests	526	(1)
Models for data from Accelerated Tests	527	(3)
Analysis of Data from Accelerated Tests	530	(1)
Reliability Assessment	531	(6)
Notes	534	(1)
Exercises	534	(3)
Reliability Improvement	537	(22)
Introduction	537	(1)
Redundancy	537	(1)
Active (Hot Standby) Redundancy	538	(4)
Full Active Redundancy	538	(2)
Partial Active Redundancy	540	(1)
Component versus System-Level Redundancy	540	(1)
Limitations of Active Redundancy	541	(1)
Cold Standby Redundancy	542	(3)
Perfect Switch	543	(1)
Imperfect Switch	544	(1)
Warm Standby Redundancy	545	(2)
Perfect Switch	545	(1)
Imperfect Switch	546	(1)
Reliability growth	547	(2)
Discrete Reliability Growth Models	549	(3)
Weiss Reliability Growth Model	549	(1)
Lloyd-Lipow Reliability Growth Model	550	(1)
Hyperbolic Model	550	(1)
Exponential Model	551	(1)
Generalized Hyperbolic Model	552	(1)
Continuous Reliability Improvement Models	552	(7)
The Duane Reliability-Growth Model	552	(2)
Gompertz Curve	554	(1)
Other Continuous Reliability-Growth Models	555	(1)
Notes	555	(1)
Exercises	556	(3)
Maintenance of Unreliable Systems	559	(30)
Introduction	559	(1)
Approaches to Maintenance	560	(4)
Reliability-Centered Maintenance	560	(3)
Total Productive Maintenance	563	(1)
Maintenance Classification and Costs	564	(3)
Maintenance Classification	564	(1)
Maintenance Costs	565	(1)
Optimal Maintenance Actions (Policies)	566	(1)
Maintenance Models at the Part Level	567	(10)
Complete Information	567	(8)
Incomplete Information---I (Component State Unknown)	575	(1)
Incomplete Information---II (Parameters Unknown)	576	(1)
Maintenance Models at the System Level	577	(6)
Model 16.1 (Discrete Time Formulation)	577	(2)
Model 16.2 (Continuous Time Formulation)	579	(2)
Model 16.3 (Point Process Formulation)	581	(2)
Maintainability and Logistics	583	(2)
Maintainability	583	(1)
Logistics	584	(1)
Maintenance Management Information Systems	585	(4)
Notes	585	(1)
Exercises	586	(3)
Warranties and Service Contracts	589	(30)
Introduction	589	(1)
Warranty---Concept and Role	590	(1)
Warranty Concept	590	(1)
Role of Warranty	590	(1)
Classification of Warranties	591	(4)
Group A Policies	592	(2)
Group B Policies	594	(1)
Group C Policies	594	(1)
Warranty Cost Analysis	595	(11)
System Characterization	595	(1)
Two Notions of Warranty Cost	596	(1)
Policy 1	597	(4)
Policy 2	601	(3)
Policy 4	604	(2)
Warranty Cost with Dynamic Sales	606	(5)
Product Sales over the Life Cycle	607	(1)
Warranty Reserves (PRW Policy)	607	(1)
Demand for Spares (FRW Policy)	608	(2)
Demand for Repairs (FRW Policy)	610	(1)
Redundancy and Product Warranty	611	(4)
Basic Relationship	611	(1)
Hot Standby (Active Redundancy)	612	(1)
Cold Standby (Passive Redundancy)	613	(2)
Extended Warranties and Service Contracts	615	(1)
Warranty Servicing	615	(4)
Notes	617	(1)
Exercises	617	(2)
Reliability Optimization	619	(42)
Introduction	619	(1)
Optimization During Design and Development	620	(8)
Optimal Reliability Allocation	620	(2)
Optimal Reliability Choice	622	(5)
Optimal Reliability Development	627	(1)
Optimization During Manufacturing	628	(11)
Optimal Testing	628	(6)
Optimal Lot Sizing	634	(5)
Optimal Maintenance of Unreliable Systems	639	(8)
Component Level Models	639	(4)
System Level Models	643	(4)
Optimal Warranty Decisions	647	(7)
Optimal Reliability and Warranty Duration	648	(1)
Optimal Repair vs Replace Strategies in Warranty Servicing	649	(2)
Cost Repair Limit Strategy	651	(3)
Analysis of an Integrated Model	654	(7)
Notes	656	(1)
Exercises	657	(4)
PART E: EPILOGUE
Case Studies	661	(32)
Introduction	661	(1)
Reliability Analysis of Aircraft Windshields	662	(19)
Background and Problem Statement	662	(1)
Data Structure and Analysis	663	(8)
Estimation of Warranty Costs	671	(5)
Sensitivity Analysis	676	(3)
Summary of Conclusions	679	(2)
Reliability Analysis of Case 2.5	681	(12)
Statement of the Problem	682	(1)
Data Analysis	682	(6)
Conclusions	688	(1)
Notes	689	(1)
Exercises	689	(4)
Resource Materials	693	(32)
Introduction	693	(1)
Journals and Conference Proceedings	693	(4)
Reliability Related Standards	697	(4)
Standards Classified by Application	697	(1)
Standards Classified by Origin	697	(2)
Handbooks	699	(1)
Sources of Information	700	(1)
Application of Standards	700	(1)
Reliability Data Bases	701	(16)
Reliability Data Base Structures	702	(1)
Component Event Data Bases	702	(8)
Incident Data Bases	710	(2)
Generic Component Reliability Data Bases	712	(3)
Data Handbooks	715	(2)
Reliability Software	717	(6)
General Statistical Software Packages	717	(1)
General Reliability Software Packages	718	(3)
Specific Reliability Software	721	(2)
Concluding Comments	723	(2)
Notes	724	(1)
Appendix A. Probability	725	(10)
A.1 Introduction to Probability Theory	725	(2)
1.1 Sample Space and Events	725	(1)
1.2 Probabilities Defined on Events	726	(1)
1.3 Conditional Probabilities	726	(1)
1.4 Random Variables	727	(1)
1.5 Distribution and Density Functions	727	(1)
A.2 Moment-Generating and Characteristic Functions	727	(1)
2.1 Moment Generating Functions	727	(1)
2.2 Characteristic Functions	728	(1)
A.3 Two or More Random Variables	728	(3)
3.1 Joint, Marginal and Conditional Distribution and Density Functions	729	(1)
3.2 Moments of Two Random Variables	729	(1)
3.3 Conditional Expectation	730	(1)
3.4 Sums of Independent Random Variables	730	(1)
3.5 Central Limit Theorem	731	(1)
A.4 Laplace Transforms	731	(1)
A.5 Functions of Random Variables	732	(3)
5.1 Asymptotic Mean and Variance of a Function of Random Variables	732	(1)
5.2 Sums of Random Variables	733	(1)
5.3 Distribution of a Product	733	(1)
5.4 Ratio of Two Random Variables	734	(1)
Appendix B. Introduction to Stochastic Processes	735	(14)
B.1 Basic Concepts	735	(2)
1.1 Stochastic Processes	735	(1)
1.2 Markov Property	735	(1)
1.3 Classification of Stochastic Processes	736	(1)
B.2 Markov Chains	737	(1)
2.1 Discrete Time Markov Chains	737	(1)
2.2 Continuous Time Markov Chains	737	(1)
B.3 Point Processes	737	(9)
3.1 Counting Processes	738	(1)
3.2 Poisson Processes	738	(2)
3.3 Renewal Processes	740	(5)
3.4 Additional Topics from Renewal Theory	745	(1)
3.5 Marked Point Process	746	(1)
B.4 Markov Processes	746	(3)
4.1 Weiner Process	746	(1)
4.2 Cumulative Process	746	(1)
4.3 General Markov Process	747	(2)
Appendix C. Statistical Tables	749	(14)
Table C1 Fractiles of the Standard Normal Distribution	749	(1)
Table C2 Fractiles of the Student-t Distribution	750	(2)
Table C3 Fractiles of the Chi-Square Distribution	752	(1)
Table C4 Factors for Two-Sided Tolerance Intervals, Normal Distribution	752	(1)
Table C5 Factors for One-Sided Tolerance Intervals, Normal Distribution	753	(1)
Table C6 Factors for Two-Sided Nonparametric Tolerance Intervals	754	(1)
Table C7 Factors for One-Sided Nonparametric Tolerance Intervals	755	(1)
Table C8 Fractiles of the F Distribution	756	(6)
Table C9 Upper Percentage Points of the Studentized Range	762	(1)
Appendix D. Basic Results on Stochastic Optimization	763	(8)
D.1 Unconstrained Static Optimization	763	(1)
D.2 Constrained Static Optimization	764	(2)
D.3 Multistage Dynamic Static Optimization	766	(1)
D.4 Continuous Time Dynamic Optimization	767	(2)
D.5 Other Topics	769	(2)
Notes	769	(2)
References	771	(26)
Author Index	797	(8)
Subject Index	805