Repairable Systems Reliability Analysis

Rajiv Nandan Rai is an assistant professor at Subir Chowdhury School of Quality and Reliability, Indian Institute of Technology Kharagpur, West Bengal, India. He obtained his PhD in Mechanical Engineering with specialization in Reliability, Maintenance and Industrial Engineering from IIT Delhi, India. He has hands on industrial experience of almost 23 years in military aviation in which he has worked at all levels of maintenance, repair and overhaul of aircraft, aero engines and their components. He has published papers in several SCI journals. S. K. Chaturvedi is a professor and currently Head at Subir Chowdhury School of Quality and Reliability, Indian Institute of Technology Kharagpur, West Bengal, India. He has research interest in the areas of reliability modeling and analysis, network reliability, life-data analysis, maintenance and optimization. He has published papers in several international journals, is reviewer to and executed several consultancy projects of private and Govt. organizations. He's written two books He's on the editorial board of Int. J. International Journal of Reliability and Safety (IJRS), Int. J of Mathematical, Engineering and Management Sciences (IJMEMS). He's also a senior member to IEEE and has also served as Co-Editor-in-Chief to International Journal of Performability Engineering. Nomesh Bolia received the PhD degree in operations research from the University of North Carolina at Chapel Hill, Chapel Hill, NC, USA. He is currently a professor in the Department of Mechanical Engineering, Indian Institute of Technology Delhi, India. His research interests include operations research and its applications to reliability, health, telecommunications, transportation and public systems. Dr. Bolia received the prestigious Indo-US Fellowship for Public Health Research and has published in several journals including IEEE Transactions.

• Series Editor Preface ixPreface xiList of Tables xvList of Figures xix1 Introduction to Repairable Systems 11.1 Introduction 11.2 Perfect, Minimal, and Imperfect Repairs 41.3 Summary 7References 82 Repairable Systems Reliability Analysis: Non-Parametric 92.1 Introduction 92.2 Mean Cumulative Function 112.3 Construction of MCF Plot and Confidence Bounds: Exact Age Data 142.3.1 MCF Construction: Exact Age Data 142.3.2 Confidence Bounds on MCF: Exact Age Data 202.3.3 Construction of MCF Plot and Confidence Bounds: Grouped Data 222.3.4 Confidence Bounds on MCF: Grouped Data 222.4 Case Study: ROV System 232.5 Interval Age Analysis 272.5.1 MCF With All Types of Failure Modes Combined 272.5.2 MCF for Individual Failure Modes 332.5.3 Exact Age Analysis 332.6 Summary and Conclusion 40References 413 Repairable Systems Reliability Analysis: Parametric 433.1 Introduction 433.2 Basic Terminologies 433.3 Parametric Analysis Approaches 463.3.1 Renewal Process 463.3.2 Non-Homogeneous Poisson Process (NHPP) 473.3.3 Generalized Renewal Process (GRP) 543.3.3.1 ARA Models 543.3.3.2 Kijima-I Model 563.3.3.3 Kijima-II Model 633.3.3.4 Virtual Age–Based Reliability Metrics 723.3.4 Summary 77References 78Further Reading 79ARI Models 794 Goodness-of-Fit Tests for Repairable Systems 834.1 Introduction 834.2 Mann’s Test for the Weibull Distribution 844.3 Laplace Trend Test 864.4 GOF Models for Power Law Process 874.4.1 Crow/AMSAA Test 874.4.2 Common Beta Hypothesis (CBH) Tests 884.4.3 CVM Test 904.5 GOF Model for GRP Based on Kijima-I Model 924.6 Summary 94References 955 Maintenance Modeling in Repairable Systems 975.1 Introduction to Maintenance Policies Using Kijima Virtual Age Model 975.2 Need for HFRC Threshold 985.3 Reliability-Based Methodology for Optimal Maintenance Policies in MA 1005.3.1 Reliability-Based Threshold Model for HFRC 1005.3.1.1 Review of Present Maintenance Policy for HFRCs 1025.4 Availability-Based HFRC Analysis 1075.4.1 Availability-Based Criteria for HFRC (BB Approach) 1075.4.1.1 Review of Overhaul Cycle (BB Approach) 1095.4.2 Availability-Based HFRC Threshold Model Considering FMs 1125.4.2.1 Maintenance Strategy for HFRCs With FM Approach 1155.4.2.2 TBO Model Considering FMs 1155.5 Summary 120References 1226 FMEA for Repairable Systems Based on Repair Effectiveness Index 1256.1 Introduction 1256.2 A Brief Overview on Performing FMEA 1286.2.1 System Definition 1296.2.2 Identification of Failure Modes 1296.2.3 Determination of Cause 1306.2.4 Assessment of Effect 1306.2.5 Classification of Severity (S) 1316.2.6 Estimation of Probability of Occurrence (O) 1316.2.7 Detection 1326.2.8 Computation of Conventional RPN 1326.2.9 Determination of Corrective Action 1326.3 Estimating RPNs Through the Modified Approach [15] 1336.4 Corrective Actions 1356.5 Summary 140References 1407 An Integrated Approach to Weapon Procurement Systems 1437.1 Introduction 1437.2 Analytic Network Process Model 1477.3 AP Index and AP Value Estimation 1517.3.1 Analytic Hierarchy Process Model 1517.3.2 AP Index Estimation 1517.3.3 Sample AP Index Estimation 1527.3.4 AP Value Estimation 1547.4 Formation of an ACU 1607.4.1 Attack Model 1607.4.2 Defense Model 1617.4.3 Illustrative Example 1627.5 Summary 164References 1668 Throughput Analysis of the Overhaul Line of a Repair Depot 1698.1 Introduction 1698.2 Basic Definitions, Parameters, and Relationships 1738.3 Variability 1748.3.1 Measures and Classes of Variability 1748.3.2 Causes of Variability 1758.3.3 Variability from Preemptive Outages (Breakdowns) 1758.3.4 Variability in Flows 1768.3.5 Variability Interactions Queuing 1778.3.5.1 The M/M/1 Queue 1778.3.5.2 The G/G/1 Queue 1788.4 Process Batching 1788.5 System Flow and Parameters 1798.6 System Analysis and Discussion 1818.6.1 Component 1: LPCR Blades 1818.6.2 Component 2: CCOC 1888.6.3 Component 3: LPTR Blades 1908.7 Summary 192References 193Appendix A 195The Saaty Rating Scale 195Pairwise Comparisons and Estimation of Weights for ANP 196Appendix B 257Unweighted Super-Matrix (Part 1) 258Unweighted Super-Matrix (Part 2) 265Weighted Super-Matrix (Part 1) 273Weighted Super-Matrix (Part 2) 280Limit Super-Matrix (Part 1) 288Limit Super-Matrix (Part 2) 295Appendix C 303Pairwise Comparisons and Estimation of Weights for AHP 304Appendix D 339F Distribution Table 339Appendix E 347Normal Distribution Table 347Appendix F 353Chi Square Table 353Appendix G 363Critical Values for Cramér-von Mises Test 363Index 365

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