RELIABILITY ENGINEERING TOPICS IN SAFETY, RELIABILITY AND QUALITY VOLUME 3 Editor A.Z. Keller, Department of Industrial Technology and Management, University of Bradford, U.K. Editorial Advisory board P. Sander, Technical University of Eindhoven, The Netherlands D.C. Barrie, Lakehead University, Ontario, Canada R. Leitch, Royal Military College of Science (Cranfield), Shriverham, U.K. Aims and Scope. Fundamental questions which are being asked these days of all products, processes and services with ever increasing frequency are: How safe? How reliable? How good is the quality? In practice none of the three topics can be considered in isolation as they often interact in subtle and complex fashions. The major objective of the series is to cover the spectrum of disciplines required to deal with safety, reliability and quality. The texts will be of a level generally suitable for final year, M.Sc and Ph.D students, researchers in the above fields, practitioners, engineers, consultants and others concerned with safety, reliability and quality. In addition to fundamental texts, authoritative 'state of the art' texts on topics of current interest will be specifically commissioned for inclusion in the series. The special emphasis which will be placed on all texts will be, readability, clarity, relevance and applicability. The titles published in this series are listed at the end of this volume. Reliability Engineering by K. K. AGGARWAL Centre for Excellence in Reliability Engineering. Regional Engineering College. Kurukshetra. India SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. Library of Congress Cataloging-in-Publication Data Aggarwa 1. K. K. Re1labl1lty englneerlng I K.K. Aggarwa1. p. cm. -- (Toplcs In safety. re1 labl 11ty. and qua1lty v. 3) Inc1udes blb1lographlca1 references (p. ) and Index. ISBN 978-94-010-4852-1 ISBN 978-94-011-1928-3 (eBook) DOI 10.1007/978-94-011-1928-3 1. Re1labl1lty (Englneerlng> I. Tlt1e. II. Serles. TA168.A33 1993 620' .00452--dc20 93-33130 ISBN 978-94-010-4852-1 Printed an acid-free paper AII Rights Reserved © 1993 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1993 Softcover reprint of the hardcover 1s t edition 1993 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner. CONTENTS Preface ix Chapter 1 RELIABILITY FUNDAMENTALS 1 1.1 Introduction 1 1.2 Need for Reliability Engineering 2 1.3 Definition 4 1.4 Causes of Failures 7 1.5 Catastrophic Failures and Degradation Failures 9 1.6 Characteristic Types of Failures 11 1.7 Useful Life of Components 13 1.8 The Exponential Case of Chance Failures 15 1.9 Reliability Measures 19 1.10 Failure Data Analysis 25 Chapter 2 RELIABILITY MATHEMATICS 30 2.1 Fundamentals of Set Theory 30 2.2 Probability Theory 32 2.3 Random Variables 36 2.4 Discrete Distributions 37 2.5 Continuous Distributions 44 2.6 Stochastic Processes 50 2.7 Markov Chains 51 Chapter 3 RELIABILITY ANALYSIS OF SERIES PARALLEL SYSTEMS 59 3.1 Introduction 59 3.2 Reliability Block Diagrams 60 3.3 Series Systems 62 3.4 Parallel Systems 67 3.5 Series Parallel Systems 70 3.6 K-out-of-M Systems 73 3.7 Open and Short Circuit Failures 75 3.8 Standby Systems 81 vi Chapter 4 RELIABILITY ANALYSIS NONSERIES PARALLEL SYSTEMS 87 4.1 Introduction 87 4.2 Path Determination 89 4.3 Boolean Algebra Methods 91 4.4 A Particular Method 93 4.5 Cut Set Approach 96 4.6 Delta-Star Method 97 4.7 Logical Signal Relations Method 100 4.8 Baye's Theorem Method 103 Chapter 5 RELIABILITY PREDICTION 107 5.1 Introduction 107 5.2 Purpose 108 5.3 Classification 109 5.4 Information Sources for Failure Rate Data 109 5.5 General Requirements 111 5.6 Prediction Methodologies 113 5.7 Software Prediction Packages 120 5.8 Role and Limitation of Reliability Prediction 121 Chapter 6 RELIABILITY ALLOCATION 122 6.1 Introduction 122 6.2 Subsystems Reliability Improvement 123 6.3 Apportionment for New Units 128 6.4 Criticality 135 Chapter 7 REDUNDANCY TECHNIQUES FOR RELIABILITY OPTIMIZATION 140 7.1 Introduction 140 7.2 Signal Redundancy 141 7.3 Time Redundancy 142 7.4 Software Redundancy 142 7.5 Hardware Redundancy 143 vii Chapter 8 MAINTAINABILITY AND AVAILABILITY 153 8.1 Introduction 153 8.2 Forms of Maintenance 155 8.3 Measures of Maintainability and Availability 157 8.4 Maintainability Function 162 8.5 Availability Function 163 8.6 Two Unit Parallel System with Repair 168 8.7 Preventive Maintenance 171 8.8 Provisioning of Spares 175 Chapter 9 RELIABILITY TESTING 178 9.1 Introduction 178 9.2 Kinds of Testing 179 9.3 Component Reliability Measurements 185 9.4 Parametric Methods 189 9.5 Confidence Limits 196 9.6 Accelerated Testing 201 9.7 Equipment Acceptance Testing 209 9.8 Reliability Growth Testing 211 Chapter 10 SOFTWARE RELIABILITY 216 10.1 Importance 216 10.2 Software Reliability and Hardware Reliability 218 10.3 Failures and Faults 219 10.4 Software Reliability 225 10.5 Software Reliability Models 228 10.6 Execution Time Component 232 10.7 Calendar Time Component 241 Chapter 11 RELIABILITY ANALYSIS OF SPECIAL SYSTEMS 246 11.1 Computer Communication Networks 246 11.2 Phased Mission Systems 250 11.3 Common Cause Failures 256 11.4 Reliability and Capacity Integration 268 viii Chapter 12 ECONOMICS OF RELIABILITY ENGINEERING 272 12.1 Introduction 272 12.2 Reliability Costs 272 12.3 Effect of Reliability on Cost 274 12.4 Reliability Achievement Cost Models 276 12.5 Reliability Utility Cost Models 280 12.6 Availability Cost Models for Parallel Systems 284 12.7 Cost Effective Choice of Subsystems 285 12.8 Replacement Policies 288 Chapter 13 RELIABILITY MANAGEMENT 293 13.1 Introduction 293 13.2 Management Objectives 295 13.3 Top Management's Role in Reliability and Quality Control Programs 297 13.4 Cost Effectiveness Considerations 299 13.5 The Management Matrix 301 13.6 Reliability and Quality Control Facilities and Equipment 304 13.7 Reliability Data 306 13.8 Training 311 Chapter 14 RELIABILITYAPPLICATIONS 316 14.1 Instrument Landing System 316 14.2 Banking System 329 PROBLEMS 335 ANSWERS TO ODD NUMBERED PROBLEMS 363 REFERENCES 367 SUBJECT INDEX 378 PREFACE The growth of present day societies in population, transportation, communication and technology points towards the use of larger and more complex systems. It took man 250,000 years to arrive at agricultural revolution; 25,000 years to arrive at industrial revolution; and only 150 years to attain the space age and we really do not know where will we go from here. We know for certain, however, that the coming age will involve the use of still larger and more complex systems. The importance of reliability has assumed new dimensions in the recent years primarily because of the complexity of larger systems and the implications of their failure. Unreliability in the modern age of technology besides causing the operational inefficiency and uneconomical maintenance can also endanger human life. The transition towards thinking about Reliability is obviously difficult because it requires a change of mentality; but difficult does not mean impossible. In its most wider sense, the word Reliability has a very important meaning: Re-Liability which simply means that it is liability, not once but again and again, from designers, manufacturers, inspectors, vendors to users and on all those who are involved with a system in any way to make it reliable. Much attention is being paid, more than ever before, to the quality and reliability of engineering systems. It is of course not easy to decide how much reliability is required and how much one can afford to pay for it. However, Defence, Aeronautical, Space, and Nuclear Power generation systems are some prime examples where compromise with quality and reliability just cannot be made; for a compromise here could mean much not only in terms of money but also the loss of many precious lives. ix x Author's 20 years of experience as Reliability Educator, Researcher and Consultant made it abundantly clear that although every Industrial Organisation desired to equip its Scientists, Engineers and Managers with the knowledge of Reliability Concepts and Applications, yet this has not been achieved. A detailed study reveals that the major bottlenecks for this situation are the non-availability of qualified faculty for their continuing education programs, the non-availability of reliability related courses at most Universities or Schools, as well as the lack of availability of a good text. This made the author to put his knowledge and experience in the form of the present text book. This text is intended to be useful for senior undergraduate and graduate students in engineering schools as also for professional engineers, reliability administrators and managers. It was difficult for the author to keep away from the temptation of including many of his research papers published in the reputed journals but a very concerted effort has been made to keep the book ideally suitable for a first course or even for a novice in the discipline of reliability engineering. This text has primarily emerged from the lecture notes which the author used for delivering courses to the students at his Institution and also several courses which were organized for the engineers in the Industrial Organizations. The text has therefore, been class room tested till the qualification of acceptance testing stage. A number of solved examples have been added to make the subject clear during studies. Many problems have also been given at the end so that the reader could voluntarily test himself/herself. The answers to odd numbered problems have been given as test verification. Much of the subject matter for the text has been taken from the lecture notes of the courses which the author co-ordinated for the benefit of practising engineers. Some of the contributors to these lecture notes deserve my special acknowledgment. These are: Professor Krishna Gopal, Dr.V.K.Sharma, Ms.Shashwati and MS.Namrata of Regional Engineering College, Kurukshetra; Professor N. Viswanadham, and Professor V. V. S. Sarma of Indian Institute of Science, Bangalore; Shri A.K.Sinha and Shri P.K.Rao of Centre for Reliability Engineering, Madras; Shri Siharan De and Shri Chandragupta from Indian Space Research Organization. In addition to these lecture notes, I have drawn very heavily from several books and papers already published in the field of reliability engineering. It is my pleasure to specially mention my obligation to Balagurusamy, Dhillon, Bazovsky, Ireson,