Reliability engineering : theroy and practice

Alessandro Birolini

Seventh Edition

Reliability

Engineering

Theory and Practice

Reliability Engineering

Alessandro Birolini

Reliability Engineering

Theory and Practice

Seventh Edition

With 190 Figures, 60 Tables, 140 Examples,

and 70 Problems for Homework

123

Prof. Dr. Alessandro Birolini*

Centro Storico—Bargello

I-50122 Firenze

Tuscany, Italy

[email protected]

www.ethz.ch/people/whoiswho,

www.birolini.ch

*

Ingénieur et penseur, Ph.D., Professor Emeritus of Reliability Eng.

at the Swiss Federal Institute of Technology (ETH), Zurich

ISBN 978-3-642-39534-5 ISBN 978-3-642-39535-2 (eBook)

DOI 10.1007/978-3-642-39535-2

Springer Heidelberg New York Dordrecht London

Library of Congress Control Number: 2013945800

Springer-Verlag Berlin Heidelberg 1994, 1997, 1999, 2004, 2007, 2010, 2014

This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of

the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,

recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or

information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar

methodology now known or hereafter developed. Exempted from this legal reservation are brief

excerpts in connection with reviews or scholarly analysis or material supplied specifically for the

purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the

work. Duplication of this publication or parts thereof is permitted only under the provisions of

the Copyright Law of the Publisher’s location, in its current version, and permission for use must

always be obtained from Springer. Permissions for use may be obtained through RightsLink at the

Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law.

The use of general descriptive names, registered names, trademarks, service marks, etc. in this

publication does not imply, even in the absence of a specific statement, that such names are exempt

from the relevant protective laws and regulations and therefore free for general use.

While the advice and information in this book are believed to be true and accurate at the date of

publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for

any errors or omissions that may be made. The publisher makes no warranty, express or implied, with

respect to the material contained herein.

Printed on acid-free paper

Springer is part of Springer Science+Business Media (www.springer.com)

"La chance vient à l'esprit qui est prêt à la recevoir." 1)

Louis Pasteur

"Quand on aperçoit combien la somme de nos

"ignorances dépasse celle de nos connaissances,

"on se sent peu porté à conclure trop vite." 2)

Louis De Broglie

"One has to learn to consider causes rather than

"symptoms of undesirable events and avoid hypo-

"critical attitudes."

Alessandro Birolini

1) "Opportunity comes to the intellect which is ready to receive it."

2) "When one recognizes how much the sum of our ignorance

2) "exceeds that of our knowledge, one is less ready to draw rapid

2) "conclusions."

Preface to the 7th Edition

The large interest granted to the 6th edition (over 2000 on-line requests per year) incited me for a 7th

and last edition of this book (11 editions with the 4 German editions 1985 - 97).

The book shows how to build in, evaluate, and demonstrate reliability, maintainability, and

availability of components, equipment, and systems. It presents the state-of-the-art of reliability

engineering, both in theory and practice, and is based on the author's more than 30 years experience

in this field, half in industry (part of which in setting up the Swiss Test. Lab. for VLSI, 1979 - 83 in

Neuchâtel) and half as Professor of Reliability Engineering at the Swiss Federal Institute of Technology

(ETH), Zurich. Considering that performance, dependability, cost, and time to market are key factors

for today's products and services, but also that failure of complex systems can have major safety

consequences, reliability engineering becomes a necessary support in developing and producing

complex equipment and systems.

The structure of the book has been conserved through all editions, with main Chapters 1 to 8 and

Appendices A1 to A11 (A10 & A11 since the 5th Edition 2007). Chapters 2, 4, and 6 deal carefully

with analytical investigations, Chapter 5 with design guidelines, Chapters 3 and 7 with tests,

and Chapter 8 with activities during production. Appendix A1 defines and comment on the terms

commonly used in reliability engineering. Appendices A2-A5 have been added to support managers in

answering the question of how to specify and achieve high reliability (RAMS) targets for complex

equipment and systems. Appendices A6- A8 are a compendium of probability theory, stochastic

processes, and mathematical statistics, as necessary for Chapters 2, 4, 6, and 7, consistent from a

mathematical point of view but still with reliability engineering applications in mind (demonstration of

established theorems is referred, and for all other propositions or equations, sufficient details for

complete demonstration are given). Appendix A9 includes statistical tables, Laplace transforms, and

probability charts. Appendix A10 resumes basic technological component's properties, and Appendix

A11 gives a set of 70 problems for homework.

This structure makes the book self contained as a text book for postgraduate students or courses in

industry (Fig. 1.9 on p. 24), allows a rapid access to practical results (as a desktop reference), and offers

to theoretically oriented readers all mathematical tools to continue research in this field.

The book covers many aspects of reliability engineering using a common language, and has been

improved step by step. Methods & tools are given in a way that they can be tailored to cover different

reliability requirement levels, and be used for safety analysis too. A large number of tables (60),

figures (190), and examples (210 of which 70 as problems for homework), as well as comprehensive

reference list and index, amply support the text. This last edition reviews, refines, and extends all

previous editions. New in particular includes:

• A strategy to mitigate incomplete coverage (p.255), yielding new models (Table 6.12c &d, p. 256).

• A comprehensive introduction to human reliability with a set of design guidelines to avoid human

errors (pp. 158-159) and new models combining human errors probability and time to accomplish a

task, based on semi-Markov processes (pp. 294-298).

• An improvement of the design guidelines for maintainability (pp. 154-158).

• An improvement of reliability allocation using Lagrange multiplier to consider cost aspects (p. 67).

• A comparison of four repair strategies (Table 4.4, p. 141).

• A comparison of basic models for imperfect switching (Table 6.11, p. 248).

• A refinement of approximate expressions, of concepts related to regenerative processes, and of the

use and limitations of stochastic processes in modeling reliability problems (e.g. Table 6.1, p.171).

• New is also that relevant statements and rules have been written cursive and centered on the text.

Furthermore,

• Particular importance has been given to the selection of design guidelines and rules, the devel￾opment of approximate expressions for large series-parallel systems, the careful simplification of

exact results to allow in-depth trade off studies, and the investigation of systems with complex

structure (preventive maintenance, imperfect switching, incomplete coverage, elements with more

than one failure mode, fault tolerant reconfigurable systems, common cause failures).

VII

VIII

• The central role of software quality assurance for complex equipment and systems is highlighted.

• The use of interarrival times starting by x = 0 at each occurrence of the event considered, instead of

the variable t, giving a sense to MTBF and allowing the introduction of a failure rate λ( ) x and a

mean time to failure MTTF also for repairable systems, is carefully discussed (pp. 5-6, 41, 175,

316, 341, 378, 380) and consequently applied. Similar is for the basic difference between failure

rate, (probability) density, and renewal density or intensity of a point process (pp. 7, 378, 426, 466,

524). In this context, the assumption as-good-as-new after repair is critically discussed wherever

necessary, and the historical distinction between nonrepairable and repairable items is scaled down

(removed for reliability function, failure rate, MTTF, and MTBF); national and international

standards should better consider this fact and avoid definitions intrinsically valid only for constant

(time independent) failure rates.

• Also valid is the introduction since the 1st edition of indices Si for reliability figures at system level

(e. g. MTTF , Si) where S stands for system and i is the state entered at t = 0 (system referring to the

highest integration level of the item considered, and t = 0 being the beginning of observations, x = 0

for interarrival times). This is mandatory for judicious investigations at the system level.

• In agreement with the practical applications, MTBF is reserved for MTBF = 1 / λ.

• Important prerequisites for accelerated tests are carefully discussed (pp. 329-334), in particular to

transfer an acceleration factor A from the MTTF ( ) MTTF MTTF A. 1 2 = to the (random) failure￾free time τ ( ) τ . τ 1 2 = A .

• Asymptotic & steady-state is used for stationary, by assuming irreducible embedded chains; repair

for restoration, by neglecting administrative, logistical, technical delays; mean for expected value.

For reliability applications, pairwise independence assures, in general, totally (mutually, statisti￾cally, stochastically) independence, independent is thus used for totally independent.

The book has growth from about 400 to 600 pages, with main improvements in the 4th to 7th Editions.

• 4th Edition: Complete review and general refinements.

• 5th Edition: Introduction to phased-mission systems, common cause failures, Petri nets, dynamic

FTA, nonhomogeneous Poisson processes, and trend tests; problems for homework.

• 6th Edition: Proof of Eqs. (6.88) & (6.94), introduction to network reliability, event trees & binary

decision diagrams, extensions of maintenance strategies and incomplete coverage,

refinements for large complex systems and approximate expressions.

The launching of the 6th Edition of this book coincided with my 70th anniversary, this was

celebrated with a special Session at the 12th Int. Conf. on Quality and Dependability CCF2010 held in

Sinaia (RO), 22-24 September 2010. My response to the last question at the interview [1.0] given to

Prof. Dr. Ioan C. Bacivarov, Chairman of the International Scientific Committee of CCF2010, can help

to explain the acceptance of this book:

"Besides more than 15 years experience in the industry, and a predisposition to be a self-taught

man, my attitude to life was surely an important key for the success of my book. This is best

expressed in the three sentences given on the first page of this book. These sentences, insisting

on generosity, modesty and responsibility apply quite general to a wide class of situations and

people, from engineers to politicians, and it is to hope that the third sentence, in particular, will

be considered by a growing number of humans, now, in front of the ecological problems we are

faced and in front of the necessity to create a federal world wide confederation of democratic

states in which freedom is primarily respect for the other."

The comments of many friends and the agreeable cooperation with Springer-Verlag are gratefully

acknowledged. Looking back to all editions (1st German 1985), thanks are due, in particular, to K.P.

LaSala for reviewing the 4th & 6th Editions [1.17], I.C. Bacivarov for reviewing the 6th Edition [1.0],

book reviewers of the German editions, P. Franken and I. Kovalenko for commenting Appendices A6-

A8, A. Bobbio F. Bonzanigo, M. Held for supporting numerical evaluations, J. Thalhammer for

supporting the edition of all figures, and L. Lambert for reading final manuscripts.

Zurich and Florence, September 13, 2013 Alessandro Birolini

Contents

1 Basic Concepts, Quality &Reliability (RAMS) Assurance of Complex Equip. & Systems . . 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.1 Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.2 Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.3 Failure Rate, MTTF, MTBF . . . . . . . . . . . . . . . . . . . . . . 4

1.2.4 Maintenance, Maintainability . . . . . . . . . . . . . . . . . . . . . 8

1.2.5 Logistic Support . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.2.6 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.2.7 Safety, Risk, and Risk Acceptance . . . . . . . . . . . . . . . . . . . 9

1.2.8 Quality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.2.9 Cost and System Effectiveness. . . . . . . . . . . . . . . . . . . . 11

1.2.10 Product Liability . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.2.11 Historical Development . . . . . . . . . . . . . . . . . . . . . . . 16

1.3 Basic Tasks & Rules for Quality & Rel. (RAMS) Assurance of Complex Eq. & Systems . 17

1.3.1 Quality and Reliability (RAMS) Assurance Tasks . . . . . . . . . . . . . 17

1.3.2 Basic Quality and Reliability (RAMS) Assurance Rules . . . . . . . . . . . 19

1.3.3 Elements of a Quality Assurance System. . . . . . . . . . . . . . . . . . 21

1.3.4 Motivation and Training . . . . . . . . . . . . . . . . . . . . . . . 24

2 Reliability Analysis During the Design Phase (Nonrepairable Elements up to System Failure) . . 25

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.2 Predicted Reliability of Equipment and Systems with Simple Structure . . . . . . . 28

2.2.1 Required Function . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.2.2 Reliability Block Diagram . . . . . . . . . . . . . . . . . . . . . . 28

2.2.3 Operating Conditions at Component Level, Stress Factors . . . . . . . . . 33

2.2.4 Failure Rate of Electronic Components . . . . . . . . . . . . . . . . . 35

2.2.5 Reliability of One-Item Structures . . . . . . . . . . . . . . . . . . . 39

2.2.6 Reliability of Series-Parallel Structures . . . . . . . . . . . . . . . . . 41

2.2.6.1 Systems without Redundancy . . . . . . . . . . . . . . . . . 41

2.2.6.2 Concept of Redundancy . . . . . . . . . . . . . . . . . . . 42

2.2.6.3 Parallel Models . . . . . . . . . . . . . . . . . . . . . . 43

2.2.6.4 Series- Parallel Structures . . . . . . . . . . . . . . . . . . 45

2.2.6.5 Majority Redundancy . . . . . . . . . . . . . . . . . . . . 49

2.2.7 Part Count Method . . . . . . . . . . . . . . . . . . . . . . . . . 51

2.3 Reliability of Systems with Complex Structure . . . . . . . . . . . . . . . . . 52

2.3.1 Key Item Method . . . . . . . . . . . . . . . . . . . . . . . . . 52

2.3.1.1 Bridge Structure . . . . . . . . . . . . . . . . . . . . . . 53

2.3.1.2 Rel. Block Diagram in which Elements Appear More than Once . . . 54

2.3.2 Successful Path Method . . . . . . . . . . . . . . . . . . . . . . . 55

2.3.3 State Space Method . . . . . . . . . . . . . . . . . . . . . . . . 56

2.3.4 Boolean Function Method . . . . . . . . . . . . . . . . . . . . . . 57

2.3.5 Parallel Models with Constant Failure Rates and Load Sharing . . . . . . . 61

2.3.6 Elements with more than one Failure Mechanism or one Failure Mode . . . . 64

2.3.7 Basic Considerations on Fault Tolerant Structures . . . . . . . . . . . . 66

2.4 Reliability Allocation and Optimization . . . . . . . . . . . . . . . . . . . 67

IX

X Contents

2.5 Mechanical Reliability, Drift Failures . . . . . . . . . . . . . . . . . . . . 68

2.6 Failure Modes Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . 72

2.7 Reliability Aspects in Design Reviews . . . . . . . . . . . . . . . . . . . . 77

3 Qualification Tests for Components and Assemblies . . . . . . . . . . . . . . . . 81

3.1 Basic Selection Criteria for Electronic Components . . . . . . . . . . . . . . . 81

3.1.1 Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

3.1.2 Performance Parameters . . . . . . . . . . . . . . . . . . . . . . 84

3.1.3 Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

3.1.4 Manufacturing Quality . . . . . . . . . . . . . . . . . . . . . . . 86

3.1.5 Long-Term Behavior of Performance Parameters . . . . . . . . . . . . . 86

3.1.6 Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

3.2 Qualification Tests for Complex Electronic Components . . . . . . . . . . . . . 87

3.2.1 Electrical Test of Complex ICs . . . . . . . . . . . . . . . . . . . . 88

3.2.2 Characterization of Complex ICs . . . . . . . . . . . . . . . . . . . 90

3.2.3 Environmental and Special Tests of Complex ICs . . . . . . . . . . . . . 92

3.2.4 Reliability Tests . . . . . . . . . . . . . . . . . . . . . . . . . . 101

3.3 Failure Modes, Mechanisms, and Analysis of Electronic Components . . . . . . . 101

3.3.1 Failure Modes of Electronic Components . . . . . . . . . . . . . . . . 101

3.3.2 Failure Mechanisms of Electronic Components . . . . . . . . . . . . . 102

3.3.3 Failure Analysis of Electronic Components . . . . . . . . . . . . . . . 102

3.3.4 Present VLSI Production-Related Reliability Problems . . . . . . . . . . 106

3.4 Qualification Tests for Electronic Assemblies . . . . . . . . . . . . . . . . . 107

4 Maintainability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

4.1 Maintenance, Maintainability . . . . . . . . . . . . . . . . . . . . . . . 112

4.2 Maintenance Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

4.2.1 Fault Detection (Recognition) and Localization. . . . . . . . . . . . . . 116

4.2.2 Equipment and Systems Partitioning . . . . . . . . . . . . . . . . . . 118

4.2.3 User Documentation . . . . . . . . . . . . . . . . . . . . . . . . 118

4.2.4 Training of Operation and Maintenance Personnel . . . . . . . . . . . . 119

4.2.5 User Logistic Support . . . . . . . . . . . . . . . . . . . . . . . 119

4.3 Maintainability Aspects in Design Reviews . . . . . . . . . . . . . . . . . . 121

4.4 Predicted Maintainability . . . . . . . . . . . . . . . . . . . . . . . . . 121

4.4.1 Calculation of MTTRS . . . . . . . . . . . . . . . . . . . . . . . 121

4.4.2 Calculation of MTTPMS . . . . . . . . . . . . . . . . . . . . . . 125

4.5 Basic Models for Spare Parts Provisioning . . . . . . . . . . . . . . . . . . 125

4.5.1 Centralized Logistic Support, Nonrepairable Spare Parts . . . . . . . . . . 125

4.5.2 Decentralized Logistic Support, Nonrepairable Spare Parts . . . . . . . . . 129

4.5.3 Repairable Spare Parts . . . . . . . . . . . . . . . . . . . . . . . 130

4.6 Maintenance Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . 134

4.6.1 Complete renewal at each maintenance action . . . . . . . . . . . . . . 134

4.6.2 Block replacement with minimal repair at failure . . . . . . . . . . . . . 138

4.6.3 Further considerations on maintenance strategies . . . . . . . . . . . . 139

4.7 Basic Cost Considerations . . . . . . . . . . . . . . . . . . . . . . . . 142

5 Design Guidelines for Reliability, Maintainability, and Software Quality . . . . . . . 144

5.1 Design Guidelines for Reliability . . . . . . . . . . . . . . . . . . . . . . 144

5.1.1 Derating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

Contents XI

5.1.2 Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

5.1.3 Moisture . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

5.1.4 Electromagnetic Compatibility, ESD Protection . . . . . . . . . . . . . 148

5.1.5 Components and Assemblies . . . . . . . . . . . . . . . . . . . . . 150

5.1.5.1 Component Selection . . . . . . . . . . . . . . . . . . . . 150

5.1.5.2 Component Use . . . . . . . . . . . . . . . . . . . . . . 150

5.1.5.3 PCB and Assembly Design . . . . . . . . . . . . . . . . . . 151

5.1.5.4 PCB and Assembly Manufacturing . . . . . . . . . . . . . . . 152

5.1.5.5 Storage and Transportation . . . . . . . . . . . . . . . . . . 153

5.1.6 Particular Guidelines for IC Design and Manufacturing . . . . . . . . . . 153

5.2 Design Guidelines for Maintainability . . . . . . . . . . . . . . . . . . . . 154

5.2.1 General Guidelines . . . . . . . . . . . . . . . . . . . . . . . . 154

5.2.2 Testability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

5.2.3 Connections, Accessibility, Exchangeability . . . . . . . . . . . . . . . 157

5.2.4 Adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

5.2.5 Human, Ergonomic, and Safety Aspects . . . . . . . . . . . . . . . . 158

5.3 Design Guidelines for Software Quality . . . . . . . . . . . . . . . . . . . 159

5.3.1 Guidelines for Software Defect Prevention . . . . . . . . . . . . . . . 162

5.3.2 Configuration Management . . . . . . . . . . . . . . . . . . . . . 165

5.3.3 Guidelines for Software Testing . . . . . . . . . . . . . . . . . . . 166

5.3.4 Software Quality Growth Models . . . . . . . . . . . . . . . . . . . 166

6 Reliability and Availability of Repairable Systems . . . . . . . . . . . . . . . . 169

6.1 Introduction, General Assumptions, Conclusions . . . . . . . . . . . . . . . 169

6.2 One-Item Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

6.2.1 One-Item Structure New at Time t = 0 . . . . . . . . . . . . . . . . . 176

6.2.1.1 Reliability Function . . . . . . . . . . . . . . . . . . . . . 176

6.2.1.2 Point Availability . . . . . . . . . . . . . . . . . . . . . 177

6.2.1.3 Average Availability . . . . . . . . . . . . . . . . . . . . 178

6.2.1.4 Interval Reliability . . . . . . . . . . . . . . . . . . . . . 179

6.2.1.5 Special Kinds of Availability . . . . . . . . . . . . . . . . . 180

6.2.2 One-Item Structure New at Time t = 0 and with Constant Failure Rate λ . . . 183

6.2.3 One-Item Structure with Arbitrary Conditions at t = 0 . . . . . . . . . . 184

6.2.4 Asymptotic Behavior . . . . . . . . . . . . . . . . . . . . . . . 185

6.2.5 Steady-State Behavior . . . . . . . . . . . . . . . . . . . . . . . . 187

6.3 Systems without Redundancy . . . . . . . . . . . . . . . . . . . . . . . . 189

6.3.1 Series Structure with Constant Failure and Repair Rates . . . . . . . . . . 189

6.3.2 Series Structure with Constant Failure and Arbitrary Repair Rates . . . . . . 192

6.3.3 Series Structure with Arbitrary Failure and Repair Rates . . . . . . . . . . 193

6.4 1-out-of-2 Redundancy (Warm, one Repair Crew) . . . . . . . . . . . . . . . . 196

6.4.1 1-out-of-2 Redundancy with Constant Failure and Repair Rates . . . . . . . 196

6.4.2 1-out-of-2 Redundancy with Constant Failure and Arbitrary Rep. Rates . . . . 204

6.4.3 1-out-of-2 Red. with Const. Failure Rate in Reserve State & Arbitr. Rep. Rates . 207

6.5 k-out-of-n Redundancy (Warm, Identical Elements, one Repair Crew) . . . . . . . . 213

6.5.1 k-out-of-n Redundancy with Constant Failure and Repair Rates . . . . . . . 214

6.5.2 k-out-of-n Redundancy with Constant Failure and Arbitrary Repair Rates . . . 218

6.6 Simple Series- Parallel Structures (one Repair Crew) . . . . . . . . . . . . . . 220

6.7 Approximate Expressions for Large Series - Parallel Structures . . . . . . . . . . 226

6.7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

6.7.2 Application to a Practical Example . . . . . . . . . . . . . . . . . . 230

XII Contents

6.8 Systems with Complex Structure (one Repair Crew) . . . . . . . . . . . . . . . 238

6.8.1 General Considerations . . . . . . . . . . . . . . . . . . . . . . . 238

6.8.2 Preventive Maintenance . . . . . . . . . . . . . . . . . . . . . . . 240

6.8.3 Imperfect Switching. . . . . . . . . . . . . . . . . . . . . . . . 243

6.8.4 Incomplete Coverage . . . . . . . . . . . . . . . . . . . . . . . . 249

6.8.5 Elements with more than two States or one Failure Mode . . . . . . . . . 257

6.8.6 Fault Tolerant Reconfigurable Systems . . . . . . . . . . . . . . . . 259

6.8.6.1 Ideal Case . . . . . . . . . . . . . . . . . . . . . . . . 259

6.8.6.2 Time Censored Reconfiguration (Phased-Mission Systems) . . . . . . 259

6.8.6.3 Failure Censored Reconfiguration . . . . . . . . . . . . . . 266

6.8.6.4 Reward and Frequency / Duration Aspects . . . . . . . . . . . 270

6.8.7 Systems with Common Cause Failures . . . . . . . . . . . . . . . . 271

6.8.8 Basic Considerations on Network-Reliability . . . . . . . . . . . . 275

6.8.9 General Procedure for Modeling Complex Systems . . . . . . . . . . . 277

6.9 Alternative Investigation Methods . . . . . . . . . . . . . . . . . . . . . 280

6.9.1 Systems with Totally Independent Elements . . . . . . . . . . . . . . 280

6.9.2 Static and Dynamic Fault Trees . . . . . . . . . . . . . . . . . . . 280

6.9.3 Binary Decision Diagrams . . . . . . . . . . . . . . . . . . . . . . . 283

6.9.4 Event Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286

6.9.5 Petri Nets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287

6.9.6 Numerical Reliability and Availability Computation . . . . . . . . . 289

6.9.6.1 Numerical Computation of System's Reliability and Availability . . . 289

6.9.6.2 Monte Carlo Simulations . . . . . . . . . . . . . . . . . . 290

6.9.7 Approximate expressions for Large, Complex Systems: Basic Considerations. . 293

6.10 Human Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . 294

7 Statistical Quality Control and Reliability Tests . . . . . . . . . . . . . . . . . 299

7.1 Statistical Quality Control . . . . . . . . . . . . . . . . . . . . . . . . . 299

7.1.1 Estimation of a Defective Probability p . . . . . . . . . . . . . . . . 300

7.1.2 Simple Two-sided Sampling Plans for Demonstration of a Def. Probability p . . 302

7.1.2.1 Simple Two-sided Sampling Plan . . . . . . . . . . . . . . . 303

7.1.2.2 Sequential Test . . . . . . . . . . . . . . . . . . . . . . 305

7.1.3 One-sided Sampling Plans for the Demonstration of a Def. Probability p . . . 306

7.2 Statistical Reliability Tests . . . . . . . . . . . . . . . . . . . . . . . . . 309

7.2.1 Reliability and Availability Estimation & Demon. for a given fixed Mission . . 309

7.2.2 Availability Estimation &Demonstration for Continuous Operation (steady-state) 311

7.2.2.1 Availability Estimation (Erlangian Failure-Free and/orRepair Times) . . . 311

7.2.2.2 Availability Demonstration (Erlangian Failure-Free and/orRepair Times) 313

7.2.2.3 Further Availability Evaluation Methods for Continuous Operation . . 314

7.2.3 Estimation and Demonstration of a Const. Failure Rate λ (or of MTBF =1/ ) λ . . 316

7.2.3.1 Estimation of a Constant Failure Rate λ . . . . . . . . . . . . 318

7.2.3.2 Simple Two-sided Test for the Demonstration of λ . . . . . . . . 320

7.2.3.3 Simple One-sided Test for the Demonstration of λ . . . . . . . . 324

7.3 Statistical Maintainability Tests . . . . . . . . . . . . . . . . . . . . . . . 325

7.3.1 Estimation of an MTTR . . . . . . . . . . . . . . . . . . . . . . . 325

7.3.2 Demonstration of an MTTR . . . . . . . . . . . . . . . . . . . . . 327

7.4 Accelerated Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329

7.5 Goodness-of-fit Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . 334

7.5.1 Kolmogorov-Smirnov Test . . . . . . . . . . . . . . . . . . . . . 334

7.5.2 Chi-square Test . . . . . . . . . . . . . . . . . . . . . . . . . . 338

Contents XIII

7.6 Statistical Analysis of General Reliability Data . . . . . . . . . . . . . . . . . 341

7.6.1 General considerations . . . . . . . . . . . . . . . . . . . . . . . 341

7.6.2 Tests for Nonhomogeneous Poisson Processes . . . . . . . . . . . . . . 343

7.6.3 Trend Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345

7.6.3.1 Tests of a HPP versus a NHPP with increasing intensity . . . . . . 345

7.6.3.2 Tests of a HPP versus a NHPP with decreasing intensity . . . . . . 348

7.6.3.3 Heuristic Tests to distinguish between HPP and Monotonic Trend . . . 349

7.7 Reliability Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351

8 Quality &Reliability (RAMS) Assurance During Production Phase (Basic Considerations). 357

8.1 Basic Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357

8.2 Testing and Screening of Electronic Components . . . . . . . . . . . . . . . 358

8.2.1 Testing of Electronic Components . . . . . . . . . . . . . . . . . . 358

8.2.2 Screening of Electronic Components . . . . . . . . . . . . . . . . . 359

8.3 Testing and Screening of Electronic Assemblies . . . . . . . . . . . . . . . . 362

8.4 Test and Screening Strategies, Economic Aspects . . . . . . . . . . . . . . . 364

8.4.1 Basic Considerations . . . . . . . . . . . . . . . . . . . . . . . . 364

8.4.2 Quality Cost Optimization at Incoming Inspection Level . . . . . . . . . . 367

8.4.3 Procedure to handle first deliveries . . . . . . . . . . . . . . . . . . 372

Appendices (A1-A11)

A1 Terms and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . 373

A2 Quality and Reliability (RAMS) Standards . . . . . . . . . . . . . . . . . . . 387

A2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387

A2.2 General Requirements in the Industrial Field . . . . . . . . . . . . . . . . 388

A2.3 Requirements in the Aerospace, Railway, Defense, and Nuclear Fields . . . . . . 390

A3 Definition and Realization of Quality and Reliability (RAMS) Requirements . . . . . 391

A3.1 Definition of Quality and Reliability (RAMS) Requirements . . . . . . . . . . . 391

A3.2 Realization of Quality & Reliability (RAMS) Requirements for Complex Eq. & Syst. . 393

A3.3 Elements of a Quality and Reliability (RAMS) Assurance Program . . . . . . . . 398

A3.3.1 Project Organization, Planning, and Scheduling . . . . . . . . . . . 398

A3.3.2 Quality and Reliability (RAMS) Requirements. . . . . . . . . . . . . 399

A3.3.3 Reliability, Maintainability, and Safety Analysis . . . . . . . . . . . 399

A3.3.4 Selection and Qualification of Components, Materials, Manuf. Processes . . 400

A3.3.5 Softwaer Quality Assurance . . . . . . . . . . . . . . . . . . . 400

A3.3.6 Configuration Management . . . . . . . . . . . . . . . . . . . 401

A3.3.7 Quality Tests . . . . . . . . . . . . . . . . . . . . . . . . . 402

A3.3.8 Quality Data Reporting System . . . . . . . . . . . . . . . . . . 404

A4 Checklists for Design Reviews . . . . . . . . . . . . . . . . . . . . . . . . 405

A4.1 System Design Review . . . . . . . . . . . . . . . . . . . . . . . . . 405

A4.2 Preliminary Design Reviews . . . . . . . . . . . . . . . . . . . . . . . 406

A4.3 Critical Design Review (System Level) . . . . . . . . . . . . . . . . . . . 409

A5 Requirements for Quality Data Reporting Systems . . . . . . . . . . . . . . . . 410

A6 Basic Probability Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 413

A6.1 Field of Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413

A6.2 Concept of Probability . . . . . . . . . . . . . . . . . . . . . . . . . 415

XIV Contents

A6.3 Conditional Probability, Independence . . . . . . . . . . . . . . . . . . . 418

A6.4 Fundamental Rules of Probability Theory . . . . . . . . . . . . . . . . . . 419

A6.4.1 Addition Theorem for Mutually Exclusive Events . . . . . . . . . . . 419

A6.4.2 Multiplication Theorem for Two Independent Events . . . . . . . . . 420

A6.4.3 Multiplication Theorem for Arbitrary Events . . . . . . . . . . . . . 421

A6.4.4 Addition Theorem for Arbitrary Events . . . . . . . . . . . . . . . 421

A6.4.5 Theorem of Total Probability . . . . . . . . . . . . . . . . . . . 422

A6.5 Random Variables, Distribution Functions . . . . . . . . . . . . . . . . . 423

A6.6 Numerical Parameters of Random Variables . . . . . . . . . . . . . . . . 429

A6.6.1 Expected Value (Mean) . . . . . . . . . . . . . . . . . . . . . 429

A6.6.2 Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . 432

A6.6.3 Modal Value, Quantile, Median . . . . . . . . . . . . . . . . . . 434

A6.7 Multidimensional Random Variables, Conditional Distributions . . . . . . . . . 434

A6.8 Numerical Parameters of Random Vectors . . . . . . . . . . . . . . . . . 436

A6.8.1 Covariance Matrix, Correlation Coefficient . . . . . . . . . . . . . 437

A6.8.2 Further Properties of Expected Value and Variance . . . . . . . . . . 438

A6.9 Distribution of the Sum of Indep. Positive Random Variables and of τmin , τmax . 438

A6.10 Distribution Functions used in Reliability Analysis . . . . . . . . . . . . . 441

A6.10.1 Exponential Distribution . . . . . . . . . . . . . . . . . . . 441

A6.10.2 Weibull Distribution . . . . . . . . . . . . . . . . . . . . 442

A6.10.3 Gamma Distribution, Erlangian Distribution, and χ2 -Distribution . . 444

A6.10.4 Normal Distribution . . . . . . . . . . . . . . . . . . . . 446

A6.10.5 Lognormal Distribution . . . . . . . . . . . . . . . . . . . 447

A6.10.6 Uniform Distribution . . . . . . . . . . . . . . . . . . . . 449

A6.10.7 Binomial Distribution . . . . . . . . . . . . . . . . . . . . 449

A6.10.8 Poisson Distribution . . . . . . . . . . . . . . . . . . . . 451

A6.10.9 Geometric Distribution . . . . . . . . . . . . . . . . . . . 453

A6.10.10 Hypergeometric Distribution . . . . . . . . . . . . . . . . . 454

A6.11 Limit Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . 454

A6.11.1 Laws of Large Numbers . . . . . . . . . . . . . . . . . . . 455

A6.11.2 Central Limit Theorem . . . . . . . . . . . . . . . . . . . 456

A7 Basic Stochastic-Processes Theory . . . . . . . . . . . . . . . . . . . . . . 460

A7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460

A7.2 Renewal Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . 463

A7.2.1 Renewal Function, Renewal Density . . . . . . . . . . . . . . . . 465

A7.2.2 Recurrence Times . . . . . . . . . . . . . . . . . . . . . . . 468

A7.2.3 Asymptotic Behavior . . . . . . . . . . . . . . . . . . . . . . 469

A7.2.4 Stationary Renewal Processes . . . . . . . . . . . . . . . . . . . 471

A7.2.5 Homogeneous Poisson Processes (HPP) . . . . . . . . . . . . . . . 472

A7.3 Alternating Renewal Processes . . . . . . . . . . . . . . . . . . . . . . 474

A7.4 Regenerative Processes with a Finite Number of States. . . . . . . . . . . . . 478

A7.5 Markov Processes with a Finite Number of States. . . . . . . . . . . . . . . 480

A7.5.1 Markov Chains with a Finite Number of States . . . . . . . . . . . . 480

A7.5.2 Markov Processes with a Finite Number of States . . . . . . . . . . . 482

A7.5.3 State Probabilities and Stay Times in a Given Class of States. . . . . . . 491

A7.5.3.1 Method of Differential Equations . . . . . . . . . . . . . 491

A7.5.3.2 Method of Integral Equations . . . . . . . . . . . . . . . 495

A7.5.3.3 Stationary State and Asymptotic Behavior . . . . . . . . . 496

A7.5.4 Frequency / Duration and Reward Aspects . . . . . . . . . . . . . 498

A7.5.4.1 Frequency / Duration . . . . . . . . . . . . . . . . . . 498

A7.5.4.2 Reward . . . . . . . . . . . . . . . . . . . . . . . . 500

Contents XV

A7.5.5 Birth and Death Process . . . . . . . . . . . . . . . . . . . . . 501

A7.6 Semi-Markov Processes with a Finite Number of States . . . . . . . . . . . . 505

A7.7 Semi-regenerative Processes with a Finite Number of States. . . . . . . . . . . 510

A7.8 Nonregenerative Stochastic Processes with a Countable Number of States . . . . . 515

A7.8.1 General Considerations . . . . . . . . . . . . . . . . . . . . . 515

A7.8.2 Nonhomogeneous Poisson Processes (NHPP) . . . . . . . . . . . . 516

A7.8.3 Superimposed Renewal Processes . . . . . . . . . . . . . . . . . 520

A7.8.4 Cumulative Processes . . . . . . . . . . . . . . . . . . . . . . 521

A7.8.5 General Point Processes . . . . . . . . . . . . . . . . . . . . . 523

A8 Basic Mathematical Statistics . . . . . . . . . . . . . . . . . . . . . . . . 525

A8.1 Empirical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 525

A8.1.1 Empirical Distribution Function . . . . . . . . . . . . . . . . . . 526

A8.1.2 Empirical Moments and Quantiles . . . . . . . . . . . . . . . . . 528

A8.1.3 Further Applications of the Empirical Distribution Function . . . . . . . 529

A8.2 Parameter Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 533

A8.2.1 Point Estimation . . . . . . . . . . . . . . . . . . . . . . . . 533

A8.2.2 Interval Estimation . . . . . . . . . . . . . . . . . . . . . . . 538

A8.2.2.1 Estimation of an Unknown Probability p . . . . . . . . . . 538

A8.2.2.2 Estimation of Param. λ for Exp. Distrib.: Fixed T, instant. repl. . 542

A8.2.2.3 Estimation of Param. λ for Exp. Distrib.: Fixed n, no repl. . . . 543

A8.2.2.4 Availability Estimation (Erlangian Failure-Free and/or Repair Times) 545

A8.3 Testing Statistical Hypotheses . . . . . . . . . . . . . . . . . . . . . . 547

A8.3.1 Testing an Unknown Probability p . . . . . . . . . . . . . . . . . 548

A8.3.1.1 Simple Two-sided Sampling Plan . . . . . . . . . . . . . 549

A8.3.1.2 Sequential Test . . . . . . . . . . . . . . . . . . . . 550

A8.3.1.3 Simple One-sided Sampling Plan . . . . . . . . . . . . . 551

A8.3.1.4 Availability Demonstr. (Erlangian Failure-Free and/or Rep.Times) . . 553

A8.3.2 Goodness-of-fit Tests for Completely Specified F ( ) 0 t . . . . . . . . . 555

A8.3.3 Goodness-of-fit Tests for F ( ) 0 t with Unknown Parameters . . . . . . . 558

A9 Tables and Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561

A9.1 Standard Normal Distribution . . . . . . . . . . . . . . . . . . . . . . 561

A9.2 χ2

-Distribution (Chi-Square Distribution) . . . . . . . . . . . . . . . . . 562

A9.3 t- Distribution (Student distribution) . . . . . . . . . . . . . . . . . . . . 563

A9.4 F-Distribution (Fisher distribution) . . . . . . . . . . . . . . . . . . . 564

A9.5 Table for the Kolmogorov-Smirnov Test . . . . . . . . . . . . . . . . . . 565

A9.6 Gamma Function . . . . . . . . . . . . . . . . . . . . . . . . . . . 566

A9.7 Laplace Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . 567

A9.8 Probability Charts (Probability Plot Papers) . . . . . . . . . . . . . . . . . 569

A9.8.1 Lognormal Probability Chart . . . . . . . . . . . . . . . . . . . 569

A9.8.2 Weibull Probability Chart . . . . . . . . . . . . . . . . . . . . 570

A9.8.3 Normal Probability Chart . . . . . . . . . . . . . . . . . . . . 571

A10 Basic Technological Component's Properties . . . . . . . . . . . . . . . . . . 572

A11 Problems for Homework . . . . . . . . . . . . . . . . . . . . . . . . . . 576

Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605

1 Basic Concepts, Quality and Reliability

(RAMS) Assurance of Complex Equipment

and Systems

Considering that complex equipment and systems are generally repairable, contain

redundancy and must be safe, the term reliability appears often for reliability,

maintainability, availability& safety. RAMS (in brackets) is used to point out this

wherever necessary in the text. The purpose of reliability (RAMS) engineering is to

develop methods and tools to evaluate and demonstrate reliability, maintainability,

availability, and safety of components, equipment & systems, as well as to support

development and production engineers in building in these characteristics. In order

to be cost and time effective, reliability (RAMS) engineering must be integrated in

the project activities, support quality assurance and concurrent engineering efforts,

and be performed without bureaucracy. This chapter introduces basic concepts,

shows their relationships, and discusses the tasks necessary to assure quality and re￾liability (RAMS)of complex equipment & systems with high quality and reliability

(RAMS) requirements. A comprehensive list of definitions is given in Appendix A1.

Standards for quality and reliability(RAMS) assurance are discussedinAppendixA2.

Refinements of management aspects are given in Appendices A3 - A5.

1.1 Introduction

Until the nineteen-sixties, quality targets were deemed to have been reached when

the item considered was found to be free of defects or systematic failures at the time

it left the manufacturer. The growing complexity of equipment and systems, as well

as the rapidly increasing cost incurred by loss of operation as a consequence of

failures, have brought to the forefront the aspects of reliability, maintainability,

availability, and safety. The expectation today is that complex equipment and

systems are not only free from defects and systematic failures at time t = 0

(when they are put into operation), but also perform the required function failure

free for a stated time interval and have a fail-safe behavior in case of critical or

catastrophic failures. However, the question of whether a given item will operate

without failures during a stated period of time cannot be simply answered by yes

or no, on the basis of a compliance test. Experience shows that only a probability

for this occurrence can be given. This probability is a measure of the item’s

A. Birolini, Reliability Engineering, DOI: 10.1007/978-3-642-39535-2_1,

Springer-Verlag Berlin Heidelberg 2014

1