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E-grāmata: Repairable Systems Reliability Analysis: A Comprehensive Framework

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Most of the reliability literature is directed towards non repairable systems, that is, systems that fail are discarded. This book is mainly dedicated towards providing coverage to the reliability modeling and analysis of repairable systems that are repaired and not replaced when they fail. Most of the equipment - mechanical or otherwise -are repairable and are subjected to maintenance actions- reactive or proactive- at various levels. Maintenance actions are carried out either to preserve a system or to renovate it to a specified functionable state. Maintenance actions are also characterized by the degree (perfect or imperfect) to which a system can be restored, i.e., to an ‘as good as new condition’ (AGAN), or ‘as bad as old condition’ (ABAO). Mathematically perfect repair is modeled using a renewal process (RP). Since it represents much idealized situation, this model has restricted applications in the analysis of repairable systems. At the other extreme, the ABAO repair is mathematically modelled using a Non-Homogenous Poisson Process (NHPP). These assumptions are very unrealistic for probabilistic modeling and leads to major distortions in statistical analysis.

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 the 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 aviation industry. The book also covers various multi-criteria decision-making (MCDM), integrated with repairable systems reliability analysis models to provide a much better insight into imperfect repair and maintenance data analysis. A complete chapter on an integrated framework for procurement process is added which will of a great assistance to the readers in enhancing the potential of their respective organization. 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.

Series Editor Preface ix
Preface xi
List of Tables
xv
List of Figures
xix
1 Introduction to Repairable Systems
1(8)
1.1 Introduction
1(3)
1.2 Perfect, Minimal, and Imperfect Repairs
4(3)
1.3 Summary
7(2)
References
8(1)
2 Repairable Systems Reliability Analysis: Non-Parametric
9(34)
2.1 Introduction
9(2)
2.2 Mean Cumulative Function
11(3)
2.3 Construction of MCF Plot and Confidence Bounds: Exact Age Data
14(9)
2.3.1 MCF Construction: Exact Age Data
14(6)
2.3.2 Confidence Bounds on MCF: Exact Age Data
20(2)
2.3.3 Construction of MCF Plot and Confidence Bounds: Grouped Data
22(1)
2.3.4 Confidence Bounds on MCF: Grouped Data
22(1)
2.4 Case Study: ROV System
23(4)
2.5 Interval Age Analysis
27(13)
2.5.1 MCF With All Types of Failure Modes Combined
27(6)
2.5.2 MCF for Individual Failure Modes
33(1)
2.5.3 Exact Age Analysis
33(7)
2.6 Summary and Conclusion
40(3)
References
41(2)
3 Repairable Systems Reliability Analysis: Parametric
43(40)
3.1 Introduction
43(1)
3.2 Basic Terminologies
43(3)
3.3 Parametric Analysis Approaches
46(37)
3.3.1 Renewal Process
46(1)
3.3.2 Non-Homogeneous Poisson Process (NHPP)
47(7)
3.3.3 Generalized Renewal Process (GRP)
54(1)
3.3.3.1 ARA Models
54(2)
3.3.3.2 Kijima-I Model
56(7)
3.3.3.3 Kijima-II Model
63(9)
3.3.3.4 Virtual Age-Based Reliability Metrics
72(5)
3.3.4 Summary
77(1)
References
78(1)
Further Reading
79(1)
ARI Models
79(4)
4 Goodness-of-Fit Tests for Repairable Systems
83(14)
4.1 Introduction
83(1)
4.2 Mann's Test for the Weibull Distribution
84(2)
4.3 Laplace Trend Test
86(1)
4.4 GOF Models for Power Law Process
87(5)
4.4.1 Crow/AMSAA Test
87(1)
4.4.2 Common Beta Hypothesis (CBH) Tests
88(2)
4.4.3 CVM Test
90(2)
4.5 GOF Model for GRP Based on Kijima-I Model
92(2)
4.6 Summary
94(3)
References
95(2)
5 Maintenance Modeling in Repairable Systems
97(28)
5.1 Introduction to Maintenance Policies Using Kijima Virtual Age Model
97(1)
5.2 Need for HFRC Threshold
98(2)
5.3 Reliability-Based Methodology for Optimal Maintenance Policies in MA
100(7)
5.3.1 Reliability-Based Threshold Model for HFRC
100(2)
5.3.1.1 Review of Present Maintenance Policy for HFRCs
102(5)
5.4 Availability-Based HFRC Analysis
107(13)
5.4.1 Availability-Based Criteria for HFRC (BB Approach)
107(2)
5.4.1.1 Review of Overhaul Cycle (BB Approach)
109(3)
5.4.2 Availability-Based HFRC Threshold Model Considering FMs
112(3)
5.4.2.1 Maintenance Strategy for HFRCs With FM Approach
115(1)
5.4.2.2 TBO Model Considering FMs
115(5)
5.5 Summary
120(5)
References
122(3)
6 FMEA for Repairable Systems Based on Repair Effectiveness Index
125(18)
6.1 Introduction
125(3)
6.2 A Brief Overview on Performing FMEA
128(5)
6.2.1 System Definition
129(1)
6.2.2 Identification of Failure Modes
129(1)
6.2.3 Determination of Cause
130(1)
6.2.4 Assessment of Effect
130(1)
6.2.5 Classification of Severity (S)
131(1)
6.2.6 Estimation of Probability of Occurrence (O)
131(1)
6.2.7 Detection
132(1)
6.2.8 Computation of Conventional RPN
132(1)
6.2.9 Determination of Corrective Action
132(1)
6.3 Estimating RPNs Through the Modified Approach [ 15]
133(2)
6.4 Corrective Actions
135(5)
6.5 Summary
140(3)
References
140(3)
7 An Integrated Approach to Weapon Procurement Systems
143(26)
7.1 Introduction
143(4)
7.2 Analytic Network Process Model
147(4)
7.3 AP Index and AP Value Estimation
151(9)
7.3.1 Analytic Hierarchy Process Model
151(1)
7.3.2 AP Index Estimation
151(1)
7.3.3 Sample AP Index Estimation
152(2)
7.3.4 AP Value Estimation
154(6)
7.4 Formation of an ACU
160(4)
7.4.1 Attack Model
160(1)
7.4.2 Defense Model
161(1)
7.4.3 Illustrative Example
162(2)
7.5 Summary
164(5)
References
166(3)
8 Throughput Analysis of the Overhaul Line of a Repair Depot
169(26)
8.1 Introduction
169(4)
8.2 Basic Definitions, Parameters, and Relationships
173(1)
8.3 Variability
174(4)
8.3.1 Measures and Classes of Variability
174(1)
8.3.2 Causes of Variability
175(1)
8.3.3 Variability from Preemptive Outages (Breakdowns)
175(1)
8.3.4 Variability in Flows
176(1)
8.3.5 Variability Interactions Queuing
177(1)
8.3.5.1 The M/M/1 Queue
177(1)
8.3.5.2 The G/G/1 Queue
178(1)
8.4 Process Batching
178(1)
8.5 System Flow and Parameters
179(2)
8.6 System Analysis and Discussion
181(11)
8.6.1 Component 1: LPCR Blades
181(7)
8.6.2 Component 2: CCOC
188(2)
8.6.3 Component 3: LPTR Blades
190(2)
8.7 Summary
192(3)
References
193(2)
Appendix A
The Saaty Rating Scale
195(1)
Pairwise Comparisons and Estimation of Weights for ANP
196(61)
Appendix B
257(46)
Unweighted Super-Matrix (Part 1)
258(7)
Unweighted Super-Matrix (Part 2)
265(8)
Weighted Super-Matrix (Part 1)
273(7)
Weighted Super-Matrix (Part 2)
280(8)
Limit Super-Matrix (Part 1)
288(7)
Limit Super-Matrix (Part 2)
295(8)
Appendix C
303(36)
Pairwise Comparisons and Estimation of Weights for AHP
304(35)
Appendix D
339(8)
F Distribution Table
339(8)
Appendix E
347(6)
Normal Distribution Table
347(6)
Appendix F
353(10)
Chi Square Table
353(10)
Appendix G
363(2)
Critical Values for Cramer-von Mises Test
363(2)
Index 365
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.
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