Repairable Systems Reliability Analysis: A Comprehensive Framework

This book provides an application-oriented framework for reliability modeling and analysis of repairable systems in conjunction with the procurement process of weapon systems and throughput analysis for industries. Most of the reliability literature is directed towards non-repairable systems, that is, systems that fail are discarded or replaced. This book is mainly dedicated towards providing coverage to the reliability modeling and analysis of repairable systems that undergo failure-repair cycles. This unique book provides a comprehensive framework for the modeling and analysis of repairable systems considering both the non-parametric and parametric approaches to deal with their failure data. The book presents MCF based non-parametric approach with several illustrative examples and the generalized renewal process (GRP) based arithmetic reduction of age (ARA) models along with its applications to the systems failure data from the aviation industry. A complete chapter on an integrated framework for procurement process is devoted by utilizing the concepts of multi-criteria decision-making (MCDM) techniques which will of a great assistance to the readers in enhancing the potential of their respective organizations. This book also presents FMEA methods tailored for GRP based repairs. This text has primarily emerged from the industrial experience and research work of the authors. A number of illustrations have been included to make the subject lucid and vivid even to the readers who are relatively new to this area. Besides, various examples have been provided to display the applicability of presented models and methodologies to assist the readers in applying the concepts presented in this book.

Table of Contents:
Series Editor Preface ix Preface xi List of Tables xv List of Figures xix 1 Introduction to Repairable Systems 1 1.1 Introduction 1 1.2 Perfect, Minimal, and Imperfect Repairs 4 1.3 Summary 7 References 8 2 Repairable Systems Reliability Analysis: Non-Parametric 9 2.1 Introduction 9 2.2 Mean Cumulative Function 11 2.3 Construction of MCF Plot and Confidence Bounds: Exact Age Data 14 2.3.1 MCF Construction: Exact Age Data 14 2.3.2 Confidence Bounds on MCF: Exact Age Data 20 2.3.3 Construction of MCF Plot and Confidence Bounds: Grouped Data 22 2.3.4 Confidence Bounds on MCF: Grouped Data 22 2.4 Case Study: ROV System 23 2.5 Interval Age Analysis 27 2.5.1 MCF With All Types of Failure Modes Combined 27 2.5.2 MCF for Individual Failure Modes 33 2.5.3 Exact Age Analysis 33 2.6 Summary and Conclusion 40 References 41 3 Repairable Systems Reliability Analysis: Parametric 43 3.1 Introduction 43 3.2 Basic Terminologies 43 3.3 Parametric Analysis Approaches 46 3.3.1 Renewal Process 46 3.3.2 Non-Homogeneous Poisson Process (NHPP) 47 3.3.3 Generalized Renewal Process (GRP) 54 3.3.3.1 ARA Models 54 3.3.3.2 Kijima-I Model 56 3.3.3.3 Kijima-II Model 63 3.3.3.4 Virtual Age–Based Reliability Metrics 72 3.3.4 Summary 77 References 78 Further Reading 79 ARI Models 79 4 Goodness-of-Fit Tests for Repairable Systems 83 4.1 Introduction 83 4.2 Mann’s Test for the Weibull Distribution 84 4.3 Laplace Trend Test 86 4.4 GOF Models for Power Law Process 87 4.4.1 Crow/AMSAA Test 87 4.4.2 Common Beta Hypothesis (CBH) Tests 88 4.4.3 CVM Test 90 4.5 GOF Model for GRP Based on Kijima-I Model 92 4.6 Summary 94 References 95 5 Maintenance Modeling in Repairable Systems 97 5.1 Introduction to Maintenance Policies Using Kijima Virtual Age Model 97 5.2 Need for HFRC Threshold 98 5.3 Reliability-Based Methodology for Optimal Maintenance Policies in MA 100 5.3.1 Reliability-Based Threshold Model for HFRC 100 5.3.1.1 Review of Present Maintenance Policy for HFRCs 102 5.4 Availability-Based HFRC Analysis 107 5.4.1 Availability-Based Criteria for HFRC (BB Approach) 107 5.4.1.1 Review of Overhaul Cycle (BB Approach) 109 5.4.2 Availability-Based HFRC Threshold Model Considering FMs 112 5.4.2.1 Maintenance Strategy for HFRCs With FM Approach 115 5.4.2.2 TBO Model Considering FMs 115 5.5 Summary 120 References 122 6 FMEA for Repairable Systems Based on Repair Effectiveness Index 125 6.1 Introduction 125 6.2 A Brief Overview on Performing FMEA 128 6.2.1 System Definition 129 6.2.2 Identification of Failure Modes 129 6.2.3 Determination of Cause 130 6.2.4 Assessment of Effect 130 6.2.5 Classification of Severity (S) 131 6.2.6 Estimation of Probability of Occurrence (O) 131 6.2.7 Detection 132 6.2.8 Computation of Conventional RPN 132 6.2.9 Determination of Corrective Action 132 6.3 Estimating RPNs Through the Modified Approach [15] 133 6.4 Corrective Actions 135 6.5 Summary 140 References 140 7 An Integrated Approach to Weapon Procurement Systems 143 7.1 Introduction 143 7.2 Analytic Network Process Model 147 7.3 AP Index and AP Value Estimation 151 7.3.1 Analytic Hierarchy Process Model 151 7.3.2 AP Index Estimation 151 7.3.3 Sample AP Index Estimation 152 7.3.4 AP Value Estimation 154 7.4 Formation of an ACU 160 7.4.1 Attack Model 160 7.4.2 Defense Model 161 7.4.3 Illustrative Example 162 7.5 Summary 164 References 166 8 Throughput Analysis of the Overhaul Line of a Repair Depot 169 8.1 Introduction 169 8.2 Basic Definitions, Parameters, and Relationships 173 8.3 Variability 174 8.3.1 Measures and Classes of Variability 174 8.3.2 Causes of Variability 175 8.3.3 Variability from Preemptive Outages (Breakdowns) 175 8.3.4 Variability in Flows 176 8.3.5 Variability Interactions Queuing 177 8.3.5.1 The M/M/1 Queue 177 8.3.5.2 The G/G/1 Queue 178 8.4 Process Batching 178 8.5 System Flow and Parameters 179 8.6 System Analysis and Discussion 181 8.6.1 Component 1: LPCR Blades 181 8.6.2 Component 2: CCOC 188 8.6.3 Component 3: LPTR Blades 190 8.7 Summary 192 References 193 Appendix A 195 The Saaty Rating Scale 195 Pairwise Comparisons and Estimation of Weights for ANP 196 Appendix B 257 Unweighted Super-Matrix (Part 1) 258 Unweighted Super-Matrix (Part 2) 265 Weighted Super-Matrix (Part 1) 273 Weighted Super-Matrix (Part 2) 280 Limit Super-Matrix (Part 1) 288 Limit Super-Matrix (Part 2) 295 Appendix C 303 Pairwise Comparisons and Estimation of Weights for AHP 304 Appendix D 339 F Distribution Table 339 Appendix E 347 Normal Distribution Table 347 Appendix F 353 Chi Square Table 353 Appendix G 363 Critical Values for Cramér-von Mises Test 363 Index 365