Repairable Systems Reliability Analysis E-Book

Rajiv Nandan Rai

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Performability Engineering Series
• Sprache: Englisch

Seitenzahl: 376

Veröffentlichungsjahr: 2020

Beschreibung

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.

Leseprobe

Table of Contents

Cover

Title Page

Copyright Page

Series Editor Preface

Preface

List of Tables

List of Figures

1 Introduction to Repairable Systems

1.1 Introduction

1.2 Perfect, Minimal, and Imperfect Repairs

1.3 Summary

References

2 Repairable Systems Reliability Analysis: Non-Parametric

2.1 Introduction

2.2 Mean Cumulative Function

2.3 Construction of MCF Plot and Confidence Bounds: Exact Age Data

2.4 Case Study: ROV System

2.5 Interval Age Analysis

2.6 Summary and Conclusion

Exercises

References

3 Repairable Systems Reliability Analysis: Parametric

3.1 Introduction

3.2 Basic Terminologies

3.3 Parametric Analysis Approaches

Solved Examples

Exercises

References

Further Reading

ARI Models

4 Goodness-of-Fit Tests for Repairable Systems

4.1 Introduction

4.2 Mann’s Test for the Weibull Distribution

4.3 Laplace Trend Test

4.4 GOF Models for Power Law Process

4.5 GOF Model for GRP Based on Kijima-I Model

4.6 Summary

Exercises

References

5 Maintenance Modeling in Repairable Systems

5.1 Introduction to Maintenance Policies Using Kijima Virtual Age Model

5.2 Need for HFRC Threshold

5.3 Reliability-Based Methodology for Optimal Maintenance Policies in MA

5.4 Availability-Based HFRC Analysis

5.5 Summary

Exercises

References

6 FMEA for Repairable Systems Based on Repair Effectiveness Index

6.1 Introduction

6.2 A Brief Overview on Performing FMEA

6.3 Estimating RPNs Through the Modified Approach [15]

6.4 Corrective Actions

6.5 Summary

References

7 An Integrated Approach to Weapon Procurement Systems

7.1 Introduction

7.2 Analytic Network Process Model

7.3 AP Index and AP Value Estimation

7.4 Formation of an ACU

7.5 Summary

References

8 Throughput Analysis of the Overhaul Line of a Repair Depot

8.1 Introduction

8.2 Basic Definitions, Parameters, and Relationships

8.3 Variability

8.4 Process Batching

8.5 System Flow and Parameters

8.6 System Analysis and Discussion

8.7 Summary

References

Appendix A

The Saaty Rating Scale

Pairwise Comparisons and Estimation of Weights for ANP

Appendix B

Unweighted Super-Matrix (Part 1)

Unweighted Super-Matrix (Part 2)

Weighted Super-Matrix (Part 1)

Weighted Super-Matrix (Part 2)

Limit Super-Matrix (Part 1)

Limit Super-Matrix (Part 2)

Appendix C

Pairwise Comparisons and Estimation of Weights for AHP

Appendix D

F Distribution Table

Appendix E

Normal Distribution Table

Appendix F

Chi Square Table

Appendix G

Critical Values for Cramér-von Mises Test

Index

Also of Interest

Check out these published and forthcoming titles in the Performability Engineering Series

End User License Agreement

List of Tables

Chapter 2

Table 2.1 Rotating machine failure data of Example 2.2.

Table 2.2 MCF and confidence calculations.

Table 2.3 Example 2.3—Burn-in period determination.

Table 2.4 Data for Example 2.4.

Table 2.5 List of failure categories and counts for all 53 ROVs.

Table 2.6 Failure Counts in Months Corresponding their Failure Modes.

Table 2.7 MCF calculation by combining all failure modes.

Table 2.8 MCF calculation for individual category at 24 months.

Table 2.9 A sample of collected data.

Table 2.10 Exercise 1: Failure data of three systems.

Chapter 3

Table 3.1 Time to failure data (hours) of aero engines of Example 3.2.

Table 3.2 Virtual age–based reliability metrics.

Table 3.3 Time to failure data (hours) of Example 3.4.

Table 3.4 Time to failure data (hours) of Example 3.5.

Table 3.5 Time between failures for a compressor.

Chapter 4

Table 4.1 Hypothesis tests.

Chapter 5

Table 5.1 Maintenance modeling in repairable systems.

Table 5.2 Relative outcome of the two overhaul cycles.

Table 5.3 Relative outcome of the two overhaul cycles.

Table 5.4 Comparative results of both overhaul cycles (Variant 1).

Table 5.5 Comparative results of both overhaul cycles (Variant 2).

Table 5.6 Results-failure mode wise for first overhaul cycle.

Table 5.7 Results-failure mode wise for

t

2OH

.

Table 5.8 Failure mode wise percent improvement.

Table 5.9 Comparative results of both overhaul cycles for the aero engine.

Chapter 6

Table 6.1 Extensions to standard FMEA.

Table 6.2 Failure cause-mode effect relationship.

Table 6.3 Severity rating.

Table 6.4 Occurrence rating.

Table 6.5 Failure mode wise initial RPN.

Table 6.6 Failure mode wise values of final Q.

Table 6.7 Final RPNs.

Table 6.8 FM1.

Table 6.9 FM2.

Table 6.11 Comparative results.

Chapter 7

Table 7.1 Brief literature review on WSCE using MCDM.

Table 7.2 Weights for API.

Table 7.3 Actual and scaled API values of each weapon category.

Table 7.4 APV estimation of combat force “ALPHA”.

Table 7.5 APV enhancement.

Table 7.6 API

ij

values.

Table 7.7 C

ij

(million USD), a

i

, d

i

, and m

i

.

Table 7.8 A

ij

values.

Table 7.9 Optimal x

ij

values.

Chapter 8

Table 8.1 Brief literature review on TH analysis.

Table 8.2 Required TH of the three components.

Table 8.3 Process requirements of LPCR blades repair.

Table 8.4 Process requirements of CCOC repair.

Table 8.5 Process requirements of LPTR blades repair.

Table 8.6 Component 1—LPCR blades.

Table 8.7 Component 2—CCOC.

Table 8.8 Component 3—LPTR blades.

Appendix A

Table A1 Pairwise comparison in cluster APWC WRT MF.

Table A2 Pairwise comparison in cluster APWC WRT FI.

Table A3 Pairwise comparison in cluster APWC WRT GN.

Table A4 Pairwise comparison in cluster APWC WRT AB.

Table A5 Pairwise comparison in cluster APWPC WRT MF.

Table A6 Pairwise comparison in cluster APWPC WRT FI.

Table A7 Pairwise comparison in cluster APWPC WRT AH.

Table A8 Pairwise comparison in cluster APWPC WRT RK.

Table A9 Pairwise comparison in cluster APWPC WRT AAM.

Table A10 Pairwise comparison in cluster APWPC WRT SAM.

Table A11 Pairwise comparison in cluster APWPC WRT FB.

Table A12 Pairwise comparison in cluster APWPC WRT RPV.

Table A13 Pairwise comparison in cluster APWPC WRT AB.

Table A14 Pairwise comparison in cluster APWPCH WRT MF.

Table A15 Pairwise comparison in cluster APWPCH WRT FI.

Table A16 Pairwise comparison in cluster APWPCH WRT RK.

Table A17 Pairwise comparison in cluster APWPCH WRT SAM.

Table A18 Pairwise comparison in cluster APWPCH WRT GN.

Table A19 Pairwise comparison in cluster APWPCH WRT FB.

Table A20 Pairwise comparison in cluster APWPCH WRT RPV.

Table A21 Pairwise comparison in cluster APWPCH WRT AB.

Table A22 Pairwise comparison in cluster ALT WRT MF.

Table A23 Pairwise comparison in cluster ALT WRT FI.

Table A24 Pairwise comparison in cluster ALT WRT AH.

Table A25 Pairwise comparison in cluster ALT WRT FB.

Table A26 Pairwise comparison in cluster APWC WRT FL.

Table A27 Pairwise comparison in cluster APWC WRT SA.

Table A28 Pairwise comparison in cluster APWC WRT UB.

Table A29 Pairwise comparison in cluster APWC WRT RN.

Table A30 Pairwise comparison in cluster APWC WRT SH.

Table A31 Pairwise comparison in cluster APWC WRT MOB.

Table A32 Pairwise comparison in cluster APWC WRT DIS.

Table A33 Pairwise comparison in cluster APWC WRT FPD.

Table A34 Pairwise comparison in cluster APWC WRT MR.

Table A35 Pairwise comparison in cluster APWC WRT W3.

Table A36 Pairwise comparison in cluster APWC WRT W1.

Table A37 Pairwise comparison in cluster APWC WRT W2.

Table A38 Pairwise comparison in cluster APWC WRT VER.

Table A39 Pairwise comparison in cluster APWC WRT SPD.

Table A40 Pairwise comparison in cluster APWC WRT RAP.

Table A41 Pairwise comparison in cluster APWC WRT RES.

Table A42 Pairwise comparison in cluster APWC WRT RTR.

Table A43 Pairwise comparison in cluster APWC WRT ROA.

Table A44 Pairwise comparison in cluster ALT WRT FL.

Table A45 Pairwise comparison in cluster ALT WRT SA.

Table A46 Pairwise comparison in cluster ALT WRT UB.

Table A47 Pairwise comparison in cluster ALT WRT SH.

Table A48 Pairwise comparison in cluster ALT WRT CS.

Table A49 Pairwise comparison in cluster ALT WRT REL.

Table A50 Pairwise comparison in cluster ALT WRT SPD.

Table A51 Pairwise comparison in cluster ALT WRT FL.

Table A52 Pairwise comparison in cluster ALT WRT FL.

Table A53 Pairwise comparison in cluster ALT WRT FL.

Table A54 Pairwise comparison in cluster ALT WRT FL.

Table A55 Pairwise comparison in cluster ALT WRT FL.

Table A56 Pairwise comparison in cluster ALT WRT FL.

Table A57 Pairwise comparison in cluster ALT WRT FL.

Table A58 Pairwise comparison in cluster ALT WRT FL.

Table A59 Pairwise comparison in cluster ALT WRT FL.

Table A60 Pairwise comparison in cluster ALT WRT FL.

Table A61 Pairwise comparison in cluster ALT WRT FL.

Table A62 Pairwise comparison in cluster ALT WRT FL.

Table A63 Pairwise comparison in cluster ALT WRT FL.

Table A64 Pairwise comparison in the cluster MATRIX WRTAPWC.

Table A65 Pairwise comparison in the cluster MATRIX WRTAPWPC.

Appendix C

Table C1 Comparison of APWC WRT DEFENCE.

Table C2 Comparison of APWC WRT ATTACK.

Table C3 Composite impact of AP operations on APWC.

Table C4 Comparison of APWPC WRT MF.

Table C5 Comparison of APWPC WRT FI.

Table C6 Comparison of APWPC WRT AH.

Table C7 Comparison of APWPC WRT RK.

Table C8 Comparison of APWPC WRT AAM.

Table C9 Comparison of APWPC WRT SAM.

Table C10 Comparison of APWPC WRT GN.

Table C11 Comparison of APWPC WRT FB.

Table C12 Comparison of APWPC WRT ASM.

Table C13 Comparison of APWPC WRT SSM.

Table C14 Comparison of APWPC WRT RPV.

Table C15 Comparison of APWPC WRT AB.

Table C16 Composite impact of APWPC on APWC.

Table C17 Comparison of APWPCH WRT FL.

Table C18 Comparison of APWPCH WRT SA.

Table C19 Comparison of APWPCH WRT UB.

Table C20 Comparison of APWPCH WRT RN.

Table C21 Comparison of APWPCH WRT SH.

Table C22 Comparison of APWPCH WRT CS.

Table C23 Comparison of APWPCH WRT REL.

List of Illustrations

Chapter 1

Figure 1.1 Types of repair.

Figure 1.2 Various techniques for reliability analysis.

Chapter 2

Figure 2.1 A MCF example.

Figure 2.2 An improving system.

Figure 2.3 A stable system.

Figure 2.4 A deteriorating system.

Figure 2.5 History and distribution of failures observed at age t.

Figure 2.6 MCF plot of Example 2.2.

Figure 2.7 Graphical plots of Example 2.3.

Figure 2.8 MCF with confidence bounds of Example 2.2 data.

Figure 2.9 MCF plot of Example 2.4.

Figure 2.10 A ROV. (Image taken from: https://www.pinterest.com/pin/55267618...

Figure 2.11 MCF by combining all failure modes.

Figure 2.12 Event plot for each system.

Figure 2.13 MCF plot of each system.

Figure 2.14 Grouping of systems based on performance behavior.

Figure 2.15 Event plot of all three groups.

Figure 2.16 MCF plot of all three groups.

Chapter 3

Figure 3.1 Bathtub-shaped intensity function.

Figure 3.2 Conditional probability of occurrence of failures.

Figure 3.3 Photograph of an aero engine.

Figure 3.4 Intensity function plot for Example 3.1.

Figure 3.5 Intensity function plot for Example 3.2.

Figure 3.6 Intensity function plot for Example 3.3.

Figure 3.7 Availability plot for Example 3.3.

Chapter 5

Figure 5.1 Reliability-based HFRC threshold.

Figure 5.2 Availability-based threshold for HFRC.

Figure 5.3 Flying task vs. availability.

Chapter 6

Figure 6.1 q vs. F(v

i

| v

i–1

) for FM1.

Figure 6.2 q vs. F(v

i

| v

i–1

) for FM2.

Figure 6.3 q vs. F(v

i

| v

i–1

) for FM3.

Chapter 7

Figure 7.1 Overview of the approach.

Figure 7.2 Evaluation of alternatives through ANP.

Figure 7.3 Evaluation of APE through AHP.

Chapter 8

Figure 8.1 Overview of Chapter 8.

Figure 8.2 Propagation of variability between workstations in series.

Figure 8.3 Work flow/work stations for engine overhaul line.

Figure 8.4 Work flow/work stations for LPCR blades.

Figure 8.5 Work flow/work stations for CCOC.

Figure 8.6 Work flow/work stations for LPTR blades repair.

Guide

Cover

Table of Contents

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Scrivener Publishing100 Cummings Center, Suite 541JBeverly, MA 01915-6106

Performability Engineering SeriesSeries Editors: Krishna B. Misra ([email protected])

Scope: A true performance of a product, or system, or service must be judged over the entire life cycle activities connected with design, manufacture, use and disposal in relation to the economics of maximization of dependability, and minimizing its impact on the environment. The concept of performability allows us to take a holistic assessment of performance and provides an aggregate attribute that reflects an entire engineering effort of a product, system, or service designer in achieving dependability and sustainability. Performance should not just be indicative of achieving quality, reliability, maintainability and safety for a product, system, or service, but achieving sustainability as well. The conventional perspective of dependability ignores the environmental impact considerations that accompany the development of products, systems, and services. However, any industrial activity in creating a product, system, or service is always associated with certain environmental impacts that follow at each phase of development. These considerations have become all the more necessary in the 21st century as the world resources continue to become scarce and the cost of materials and energy keep rising. It is not difficult to visualize that by employing the strategy of dematerialization, minimum energy and minimum waste, while maximizing the yield and developing economically viable and safe processes (clean production and clean technologies), we will create minimal adverse effect on the environment during production and disposal at the end of the life. This is basically the goal of performability engineering.

It may be observed that the above-mentioned performance attributes are interrelated and should not be considered in isolation for optimization of performance. Each book in the series should endeavor to include most, if not all, of the attributes of this web of interrelationship and have the objective to help create optimal and sustainable products, systems, and services.

Publishers at ScrivenerMartin Scrivener ([email protected])Phillip Carmical ([email protected])

Repairable Systems Reliability Analysis

A Comprehensive Framework

Edited by

Rajiv Nandan Rai

Indian Institute of Technology Kharagpur, Kharagpur, India

Sanjay Kumar Chaturvedi

Indian Institute of Technology Kharagpur, Kharagpur, India

Nomesh Bolia

Indian Institute of Technology Delhi, Delhi, India

This edition first published 2020 by John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA and Scrivener Publishing LLC, 100 Cummings Center, Suite 541J, Beverly, MA 01915, USA© 2020 Scrivener Publishing LLCFor more information about Scrivener publications please visit www.scrivenerpublishing.com.

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Library of Congress Cataloging-in-Publication Data

ISBN 978-1-119-52627-8

Cover image: Stockvault.ComCover design by Russell Richardson

Series Editor Preface

This is the 10th book in the series on performability engineering since the series was launched in 2014. The subject of this book is special as not many books on Repairable System Reliability are available in the literature on reliability engineering. All the three authors of this book come from the reputed academic institutes of technology in India, but have also have had rich experience of working on field projects of practical importance. Incidentally, the two of the authors, namely, Rajiv Nandan Rai and Sanjay Kumar Chaturvedi are the postgraduate and doctorate, respectively, of the first Centre of Reliability Engineering established in India by the series Editor in 1983 at the Indian institute of Technology, at Kharagpur. Rajiv Nandan Rai has also served with the Indian Air Force and has had about 20 years of industrial experience in military aviation, which is reflected in the treatment of the subject.

Actually, the research in repairable systems reliability is limited and very few textbooks are available on the subject. The available textbooks generally provide coverage of non-homogeneous Poisson process (NHPP) where the repair effectiveness index (REI) is considered one. Few more textbooks provide treatment of non-parametric reliability analysis of repairable systems. However, this book aims to provide a comprehensive framework for the analysis of repairable systems considering both the non-parametric and parametric estimation of the failure data. The book also provides discussion of generalized renewal process (GRP) based arithmetic reduction of age (ARA) models along with its applications to repairable systems data from aviation industry.

Repair actions in military aviation may not fall under ‘as good as new (AGAN)’ and ‘as bad as old (ABAO)’ assumptions which often find limited uses in practical applications. But actual situation could lie somewhere between the two. A repairable system may end up in one of the five likely states subsequent to a repair: (i) as good as new, (ii) as bad as old, (iii) better than old but worse than new, (iv) better than new, and lastly, (v) worse than old. Existing probabilistic models used in repairable system analysis, such as the perfect renewal process (PRP) and the non-homogeneous Poisson process (NHPP), account for the first two states. In the concept of imperfect repair, the repair actions are unable to bring the system to as good as new state, but can transit to a stage that is somewhere between new and that of one preceding to a failure. Because of the requirement to have more precise analyses and predictions, the GRP can be of great interest to reduce the modelling ambiguity resulting from the above repair assumptions. The authors have discussed to a great extent various possibilities under repair-ability environment and applied them to physical systems. The book also summarizes the models and approaches available in the literature on the analysis of repairable system reliability.

It is expected the book will be very useful to all those who are designing or maintaining repairable systems.

Krishna B. MisraSeries Editor

Preface

Conventionally, a repair action usually is assumed to renew a system to its “as good as new” condition. This assumption is very unrealistic for probabilistic modeling and leads to major distortions in statistical analysis. Most of the reliability literature is directed toward non-repairable systems, that is, systems that fail are discarded. This book is mainly dedicated toward providing coverage to the reliability modeling and analysis of repairable systems that are repaired and not replaced when they fail.

During his journey in the military organization, the first author realized that most of the industries desire to equip its scientists, engineers, and managers with the knowledge of reliability concepts and applications but have not been able to succeed completely. Repairable systems reliability analysis is an area where the research work is quite limited and very few text books are available. The available text books are also limited in providing a coverage only up to the concepts of non-homogeneous Poisson process (NHPP) where the repair effectiveness index (REI) is considered one. Few more textbooks provide knowledge only on non-parametric reliability analysis on repairable systems.

This book provides a comprehensive framework for the modeling and analysis of repairable systems considering both the non-parametric and parametric estimation of the failure data. The book provides due exposure to the generalized renewal process (GRP)–based arithmetic reduction of age (ARA) models along with its applications to repairable systems data from aviation industry. The book also covers various multi-criteria decision making (MCDM) techniques, 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. It is intended to be useful for senior undergraduate, graduate, and post-graduate students in engineering schools as also for professional engineers, reliability administrators, and managers.

This book has primarily emerged from the industrial experience and research work of the authors. A number of illustrations have been included to make the subject pellucid and vivid even to the readers who are new to this area. Besides, various examples have been provided to showcase the applicability of presented models and methodologies, besides, to assist the readers in applying the concepts presented in the book.

The concepts of random variable and commonly used discrete and continuous probability distributions can readily be seen in various available texts that deal with reliability analysis of non-reparable systems. The reliability literature is in plenty to cover such aspects in reliability data analysis where the failure times are modeled by appropriate life distributions. Hence, the readers are advised to refer to any such text book on non-repairable systems reliability analysis for a better comprehension of this book.

Chapter 1 presents various terminologies pertaining to repairable systems followed by the description of repair concepts and repair categories.

The mean cumulative function (MCF)–based graphical and non-parametric methods for reparable systems are simple yet powerful option available to analyze the fleet/system events recurrence behavior and their recurrence rate. Chapter 2 is dedicated to MCF-based non-parametric analysis through examples with a case study of remotely operated vehicle (ROV).

The renewal and homogeneous Poisson processes (HPPs) followed by an exhaustive description of NHPP are covered in Chapter 3 along with solved examples. Thereafter, the chapter brings out a detailed description of ARA and ARI models along with their applicability in maintenance. The chapter also derives the maximum likelihood estimators (MLEs) for Kijima virtual age models with the help of GRP. The models are demonstrated with the help of suitable examples.

Chapter 4 provides various goodness-of-fit (GOF) tests for repairable systems and their applications with examples.

Chapter 5 presents various reliability and availability-based maintenance models for repairable systems. This chapter introduces the concept of high failure rate component (HFRC)–based thresholds and provides maintenance models by considering the “Black Box” (BB) approach followed by the failure mode (FM) approach. All the models are well-supported with examples.

This book presents modified failure modes and analysis (FMEA) model in Chapter 6. This model is based on the concept of REI propounded by Kijima and is best applicable to the repairable systems reliability analysis.

Chapter 7 provides an integrated approach for weapon procurement systems for military aviation. The combined applications of MCDM tools like AHP, ANP, and optimization techniques can be seen in this chapter. This model can be used for other industries procurement policy as well.

Chapter 8 is aimed at reducing the overhaul time of a repairable equipment to enhance the availability. Various concepts of throughput analysis have been utilized in this chapter.

The book makes an honest attempt to provide a comprehensive coverage to various models and methodologies that can be used for modeling and analysis of repairable systems reliability analysis. However, there is always a scope for improvement and we are looking forward to receiving critical reviews and/or comments of the book from students, teachers, and practitioners. We hope that the readers will all gain as much knowledge, understanding, and pleasure from reading this book as we have from writing it.

Rajiv Nandan RaiSanjay Kumar ChaturvediNomesh BoliaAugust 2020

List of Tables

Table 2.1

Rotating machine failure data of Example 2.2

Table 2.2

MCF and confidence calculations

Table 2.3

Example 2.3—Burn-in period determination

Table 2.4

Data for Example 2.4

Table 2.5

List of failure categories and counts for all 53 ROVs

Table 2.6

Failure Counts in Months Corresponding their Failure Modes

Table 2.7

MCF calculation by combining all failure modes

Table 2.8

MCF calculation for individual category at 24 months

Table 2.9

A sample of collected data

Table 2.10

Exercise 1: Failure data of three systems

Table 3.1

Time to failure data (hours) of aero engines of Example 3.2

Table 3.2

Virtual age–based reliability metrics

Table 3.3

Time to failure data (hours) of Example 3.4

Table 3.4

Time to failure data (hours) of Example 3.5

Table 3.5

Time between failures for a compressor

Table 4.1

Hypothesis tests

Table 5.1

Maintenance modeling in repairable systems

Table 5.2

Relative outcome of the two overhaul cycles

Table 5.3

Relative outcome of the two overhaul cycles

Table 5.4

Comparative results of both overhaul cycles (Variant 1)

Table 5.5

Comparative results of both overhaul cycles (Variant 2)

Table 5.6

Results-failure mode wise for first overhaul cycle

Table 5.7

Results-failure mode wise for

t

2OH

Table 5.8

Failure mode wise percent improvement

Table 5.9

Comparative results of both overhaul cycles for the aero engine

Table 6.1

Extensions to standard FMEA

Table 6.2

Failure cause-mode effect relationship

Table 6.3

Severity rating

Table 6.4

Occurrence rating

Table 6.5

Failure mode wise initial RPN

Table 6.6

Failure mode wise values of final Q

Table 6.7

Final RPNs

Table 6.8

FM1

Table 6.9

FM2

Table 6.10

FM3

Table 6.11

Comparative results

Table 7.1

Brief literature review on WSCE using MCDM

Table 7.2

Weights for API

Table 7.3

Actual and scaled API values of each weapon category

Table 7.4

APV estimation of combat force “ALPHA”

Table 7.5

APV enhancement

Table 7.6

API

ij

values

Table 7.7

C

ij

(million USD), a

i

, d

i

, and m

i

Table 7.8

A

ij

values

Table 7.9

Optimal x

ij

values

Table 8.1

Brief literature review on TH analysis

Table 8.2

Required TH of the three components

Table 8.3

Process requirements of LPCR blades repair

Table 8.4

Process requirements of CCOC repair

Table 8.5

Process requirements of LPTR blades repair

Table 8.6

Component 1—LPCR blades

Table 8.7

Component 2—CCOC

Table 8.8

Component 3—LPTR blades

List of Figures

Figure 1.1

Types of repair

Figure 1.2

Various techniques for reliability analysis

Figure 2.1

A MCF example

Figure 2.2

An improving system

Figure 2.3

A stable system

Figure 2.4

A deteriorating system

Figure 2.5

History and distribution of failures observed at age t

Figure 2.6

MCF plot of Example 2.2

Figure 2.7

Graphical plots of Example 2.3

Figure 2.8

MCF with confidence bounds of Example 2.2 data

Figure 2.9

MCF plot of Example 2.4

Figure 2.10

A ROV. (Image taken from:

https://www.pinterest.com/pin/552676185495210644/?nic=1

)

Figure 2.11

MCF by combining all failure modes

Figure 2.12

Event plot for each system

Figure 2.13

MCF plot of each system

Figure 2.14

Grouping of systems based on performance behavior

Figure 2.15

Event plot of all three groups

Figure 2.16

MCF plot of all three groups

Figure 3.1

Bathtub-shaped intensity function

Figure 3.2

Conditional probability of occurrence of failures

Figure 3.3

Photograph of an aero engine

Figure 3.4

Intensity function plot for Example 3.1

Figure 3.5

Intensity function plot for Example 3.2

Figure 3.6

Intensity function plot for Example 3.3

Figure 3.7

Availability plot for Example 3.3

Figure 5.1

Reliability-based HFRC threshold

Figure 5.2

Availability-based threshold for HFRC

Figure 5.3

Flying task vs. availability

Figure 6.1

q vs. F(v

i

| v

i–1

) for FM1

Figure 6.2

q vs. F(v

i

| v

i–1

) for FM2

Figure 6.3

q vs. F(v

i

| v

i–1

) for FM3

Figure 7.1

Overview of the approach

Figure 7.2

Evaluation of alternatives through ANP

Figure 7.3

Evaluation of APE through AHP

Figure 8.1

Overview of Chapter 8

Figure 8.2

Propagation of variability between workstations in series

Figure 8.3

Work flow/work stations for engine overhaul line

Figure 8.4

Work flow/work stations for LPCR blades

Figure 8.5

Work flow/work stations for CCOC

Figure 8.6

Work flow/work stations for LPTR blades repair

1Introduction to Repairable Systems

1.1 Introduction

A system is a collection of mutually related items, assembled to perform one or more intended functions. Any system majorly consists of (i) items as the operating parts, (ii) attributes as the properties of items, and (iii) the link between items and attributes as interrelationships. A system is not only expected to perform its specified function(s) under its operating conditions and constraints but also expected to meet specified requirements, referred as performance and attributes. The system exhibits certain behavioural pattern that can never ever be exhibited by any of its constituent items or their subsets. The items of a system may themselves be systems, and every system may be part of a larger system in a hierarchy. Each system has a purpose for which items, attributes, and relationships have been organized. Everything else that remains outside the boundaries of system is considered as environment from where a system receives input (in the form of material, energy, and/or information) and makes output to the environment which might be in different form as that of the input it had received. Internally, the items communicate through input and output wherein output(s) of one items(s) becomes the input(s) to others. The inherent ability of an item/system to perform required function(s) with specified performance and attributes when it is utilized as specified is known as functionability [1]. This definition differentiates between the terms functionality and functionability where former is purely related to the function performed whereas latter also takes into considerations the level of performance achieved.

Despite the system is functionable at the beginning of its operational life, we are fully aware that even after using the perfect design, best technology available for its production or the materials from which it is made, certain irreversible changes are bound to occur due to the actions of various interacting and superimposing processes, such as corrosion, deformations, distortions, overheating, fatigue, or similar. These interacting processes are the main reason behind the change in the output characteristics of the system. The deviation of these characteristics from the specifications constitutes a failure. The failure of a system, therefore, can be defined as an event whose occurrence results in either loss of ability to perform required function(s) or loss of ability to satisfy the specified requirements (i.e., performance and/or attributes). Regardless of the reason of occurrence of this change, a failure causes system to transit from a state of functioning to a state of failure or state of unacceptable performance. For many systems, a transition to the unsatisfactory or failure state means retirement. Engineering systems of this type are known as non-maintained or non-reparable system because it is impossible to restore their functionability within reasonable time, means, and resources. For example, a missile is a non-repairable system once launched. Other examples of non-repairable systems include electric bulbs, batteries, transistors, etc. However, there are a large number of systems whose functionability can be restored by effecting certain specified tasks known as maintenance tasks. These tasks can be as complex as necessitating a complete overhaul or as simple as just cleaning, replacement, or adjustment. One can cite several examples of repairable systems one’s own day-to-day interactions with such systems that include but not limited to automobiles, computers, aircrafts, industrial machineries, etc. For instance, a laptop, not connected to an electrical power supply, may fail to start if its battery is dead. In this case, replacing the battery—a non-maintained item—with a new one may solve the problem. A television set is another example of a repairable system, which upon failure can be restored to satisfactory condition by simply replacing either the failed resistor or transistor or even a circuit board if that is the cause, or by adjusting the sweep or synchronization settings.

The system, in fact, wavers and stays between satisfactory and unsatisfactory states during its operational life until a decision is taken to dispense with it. The proportion of the time, during which the system is functionable, depends on the interaction between the inherent characteristics of a system from the design and utilization function given by the users’ specific requirements and actions. The prominent inherent characteristics could be reliability, maintainability, and supportability. Note that these characteristics are directly related to the frequency of failures, the complexity of a maintenance task, and ease to support that task. The utilization characteristics are driven by the users’ operational scenarios and maintenance policy adopted, which are further supported by the logistics functions, which is related to the provisioning of operational and maintenance resources needed. In short, the pattern followed by an engineering system can be termed as funtionability profile whose specific shape is governed by the inherent characteristics of design and system’s utilization. The metric Availability or its variants quantitatively summarize the functionability profile of an item/system. It is an extremely important and useful measure for reparable systems; besides, a technical aid in the cases where user is to make decisions regarding the acquisition of one item among several competing possibilities with differing values of reliability, maintainability, and supportability. Functionability and availability brought together indicates how good a system is. It is referred as system technical effectiveness representing the inherent capability of the system. Clearly, the biggest opportunity to make an impact on systems’ characteristics is at the design stage to won or lost the battle when changes and modifications are possible almost at negligible efforts. Therefore, the biggest challenge for engineers, scientists, and researchers has been to assess the impact of the design on the maintenance process at the earliest stage of the design through field experiences, analysis, planning and management. And, the repairable system analysis is not just constricted on finding out the reliability metrics.

Most complex systems, such as automobiles, communication systems, aircraft, engine controllers, printers, medical diagnostics systems, helicopters, train locomotives, and so on so forth are repaired once they fail. In fact, when a system enters into utilization process, it is exposed to three different performance influencing factors, viz., operation, maintenance, and logistics, which should be strategically managed in accordance with the business plans of the owners. It is often of considerable interest to determine the reliability and other performance characteristics under these conditions. Areas of interest may include assessing the expected number of failures during the warranty period, maintaining a minimum reliability for an interval, addressing the rate of wear out, determining when to replace or overhaul a system, and minimizing its life cycle costs.

Traditional reliability life or accelerated test data analysis—nonpara-metric or parametric—is based on a truly random sample drawn from a single population and independent and identically distributed (i.i.d.) assumptions on the reliability data obtained from the testing/fielded units. This i.i.d. assumption may also be valid, intuitively, on the first failure of several identical units, coming from the same design and manufacturing process, fielded in a specified or assumed to be in an identical environment. Life data of such items usually consists of an item’s single failure (or very first failure for reparable items) times with some items may be still surviving-referred as censoring or suspension. The reliability literature is in plenty to cover such aspects in reliability data analysis where the failure times are modeled by appropriate life distributions [2].

However, in repairable system, one generally has times of successive failures of a single system, often violating the i.i.d assumption. Hence, it is not surprising that statistical methods required for repairable system differ from those needed in reliability analysis of non-repairable items. In order to address the reliability characteristics of complex repairable systems, a process rather than a distribution is often used. For a repairable system, time to next failure depends on both the life distribution (the probability distribution of the time to first failure) and the impact of maintenance actions performed after the first occurrence of a failure. The most popular process model is the Power Law Process (PLP). This model is popular for several reasons. For instance, it has a very practical foundation in terms of minimal repair—a situation when the repair of a failed system is just enough to get the system operational again by repair or replacement of its constituent item(s). Second, if the time to first failure follows the Weibull distribution, then the Power Law model repair governs each succeeding failure and adequately models the minimal repair phenomenon. In other words, the Weibull distribution addresses the very first failure and the PLP addresses each succeeding failure for a repairable system. From this viewpoint, the PLP can be regarded as an extension of the Weibull distribution and a generalization of Poisson process. Besides, the PLP is generally computationally easy in providing useful and practical solutions, which have been usually comprehended and accepted by the management for many real-world applications.

The usual notion and assumption of overhauling of a system is to bringing it back to “as-good-as-new” (AGAN) condition. This notion may not be true in practice and an overhaul may not achieve the system reliability back to where it was when the system was new. However, there is concurrence among all the stakeholders that an overhaul indeed makes the system more reliable than just before its overhaul. For systems that are not overhauled, there is only one cycle and we are interested in the reliability characteristics of such systems as the system ages during its operational life. For systems that are overhauled several times during their lifetime, our interest would be in the reliability characteristics of the system as it ages during its cycles, i.e., the age of the system starts from the beginning of the cycle and each cycle starts with a new zero time.

1.2 Perfect, Minimal, and Imperfect Repairs

As discussed earlier, a repairable system is a system that is restored to its functionable state after the loss of functionability by the actions other than replacement of the entire system. The quantum of repair depends upon various factors like criticality of the component failed, operational status of the system, risk index, etc. Accordingly, the management takes a decision on how much repair a system has to undergo. The two extremes of the repair are perfect and minimal repairs. A system is said to be perfectly repaired, if the system is restored to AGAN condition (as it is replaced with a new one). Normally, a perfect repair in terms of the replacement is carried out for very critical components, which may compromise operation ability, safety of the system, and/or personnel working with the system. On the other hand, a system is said to be minimally repaired, if its working state is restored to “as-bad-as-old” (ABAO). This type of repair is undertaken when there is heavy demand for the system to work for a finite time or the system will be undergoing preventive maintenance shortly or will be scrapped soon.