Reliability Engineering and Risk Analysis : A Practical Guide

523 Pages·2017·9.497 MB·English

by  Mohammad Modarres, Mark P. Kaminskiy, Vasiliy Krivtsov

THIRD EDITION
RELIABILITY
ENGINEERING
and
RISK ANALYSIS
A Practical Guide

T H I R D E D I T I O N
RELIABILITY
ENGINEERING
and
RISK ANALYSIS
A Practical Guide
Mohammad Modarres
Mark P. Kaminskiy
Vasiliy Krivtsov
Boca Raton London New York
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Library of Congress Cataloging‑in‑Publication Data
Names: Modarres, M. (Mohammad), author. | Kaminskiy, Mark, 1946- author. |
Krivtsov, Vasiliy, 1963- author.
Title: Reliability engineering and risk analysis : a practical guide /
Mohammad Modarres, Mark P. Kaminskiy, Vasiliy Krivtsov.
Description: Third edition. | Boca Raton : Taylor & Francis, a CRC title,
part of the Taylor & Francis imprint, a member of the Taylor & Francis
Group, the academic division of T&F Informa, plc, 2017.
Identifiers: LCCN 2016038161 | ISBN 9781498745871
Subjects: LCSH: Reliability (Engineering) | Risk assessment.
Classification: LCC TA169 .M627 2017 | DDC 620/.00452--dc23
LC record available at https://lccn.loc.gov/2016038161
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
Contents
Preface to the Third Edition ..........................................................................................................xiii
Acknowledgments ............................................................................................................................xv
Authors ...........................................................................................................................................xvii
Chapter 1 Reliability Engineering in Perspective .........................................................................1
1.1 Why Study Reliability? .....................................................................................1
1.2 Failure Models ...................................................................................................1
1.2.1 Stress–Strength Model .........................................................................2
1.2.2 Damage–Endurance Model ..................................................................2
1.2.3 Performance–Requirement Model .......................................................3
1.3 Failure Mechanisms ..........................................................................................3
1.4 Performance Measures ......................................................................................7
1.5 Formal Definition of Reliability ......................................................................11
1.6 Definition of Availability .................................................................................12
1.7 Definition of Risk ............................................................................................13
References ..................................................................................................................13
Chapter 2 Basic Reliability Mathematics: Review of Probability and Statistics ........................15
2.1 Introduction .....................................................................................................15
2.2 Elements of Probability ...................................................................................15
2.2.1 Sets and Boolean Algebra ..................................................................15
2.2.2 Basic Laws of Probability ..................................................................18
2.2.2.1 Classical Interpretation of Probability
(Equally Likely Concept)....................................................19
2.2.2.2 Frequency Interpretation of Probability .............................19
2.2.2.3 Subjective Interpretation of Probability .............................20
2.2.2.4 Calculus of Probability .......................................................20
2.2.3 Bayes’ Theorem ..................................................................................24
2.3 Probability Distributions .................................................................................28
2.3.1 Random Variable ................................................................................28
2.3.2 Some Basic Discrete Distributions .....................................................29
2.3.2.1 Discrete Uniform Distribution ............................................29
2.3.2.2 Binomial Distribution .........................................................29
2.3.2.3 Hypergeometric Distribution ..............................................31
2.3.2.4 Poisson’s Distribution .........................................................32
2.3.2.5 Geometric Distribution .......................................................33
2.3.3 Some Basic Continuous Distributions ................................................34
2.3.3.1 Normal Distribution ............................................................36
2.3.3.2 Lognormal Distribution ......................................................38
2.3.3.3 Exponential Distribution .....................................................39
2.3.3.4 Weibull Distribution ...........................................................40
2.3.3.5 Gamma Distribution ...........................................................41
2.3.3.6 Beta Distribution .................................................................42
2.3.3.7 Beta-Exponential Distribution ............................................43
2.3.4 Joint and Marginal Distributions........................................................43
2.3.5 Truncated Distributions ......................................................................46
v
vi Contents
2.4 Basic Characteristics of Random Variables ....................................................47
2.5 Estimation and Hypothesis Testing .................................................................53
2.5.1 Point Estimation .................................................................................53
2.5.1.1 Method of Moments ............................................................54
2.5.1.2 Maximum Likelihood Method ...........................................55
2.5.2 Interval Estimation and Hypothesis Testing ......................................56
2.5.2.1 Hypothesis Testing ..............................................................57
2.5.3 Bayesian Estimation ...........................................................................58
2.6 Frequency Tables and Histograms ..................................................................59
2.7 Goodness-of-Fit Tests ......................................................................................61
2.7.1 Chi-Square Test ..................................................................................61
2.7.2 Kolmogorov–Smirnov Test ................................................................64
2.8 Regression Analysis.........................................................................................65
2.8.1 Simple Linear Regression ..................................................................66
References ..................................................................................................................74
Chapter 3 Component Reliability Analysis ................................................................................75
3.1 Concept of Reliability ......................................................................................75
3.1.1 Reliability Function ............................................................................75
3.1.2 Failure Rate ........................................................................................77
3.1.3 Some Useful Bounds and Inequalities for IFR (DFR) .......................82
3.1.3.1 Bounds Based on a Known Quantile ..................................82
3.1.3.2 Bounds Based on a Known Mean .......................................83
3.1.3.3 Inequality for Coefficient of Variation ...............................83
3.2 Common Distributions in Component Reliability ...........................................83
3.2.1 Exponential Distribution ....................................................................83
3.2.2 Weibull Distribution ...........................................................................84
3.2.3 Gamma Distribution ...........................................................................85
3.2.4 Normal Distribution ...........................................................................86
3.2.5 Lognormal Distribution......................................................................87
3.2.6 Extreme Value Distributions ..............................................................87
3.2.6.1 Some Basic Concepts and Definitions ................................87
3.2.6.2 Order Statistics from Samples of Random Size .................88
3.2.6.3 Asymptotic Distributions of Maxima and Minima ............89
3.2.6.4 Three Types of Limit Distributions ....................................89
3.3 Reliability Data and Model Selection ..............................................................92
3.3.1 Graphical Nonparametric Procedures ................................................92
3.3.1.1 Small Samples ....................................................................92
3.3.1.2 Large Samples ....................................................................93
3.3.2 Probability Plotting ............................................................................95
3.3.2.1 Exponential Distribution Probability Plotting ....................96
3.3.2.2 Weibull Distribution Probability Plotting ...........................97
3.3.2.3 Normal and Lognormal Distribution Probability Plotting......99
3.3.3 Total-Time-on-Test Plots ..................................................................101
3.4 Maximum Likelihood Estimation of Reliability Distribution Parameters ...103
3.4.1 Censored Data ..................................................................................104
3.4.1.1 Left and Right Censoring .................................................104
3.4.1.2 Type I Censoring ..............................................................104
3.4.1.3 Type II Censoring .............................................................105
3.4.1.4 Types of Reliability Tests .................................................105
Contents vii
3.4.1.5 Random Censoring ...........................................................105
3.4.1.6 Maximum Likelihood Estimation Using
Reliability Data ................................................................105
3.4.2 Exponential Distribution Point Estimation ......................................109
3.4.2.1 Type I Life Test with Replacement ...................................109
3.4.2.2 Type I Life Test without Replacement ..............................109
3.4.2.3 Type II Life Test with Replacement ..................................109
3.4.2.4 Type II Life Test without Replacement.............................110
3.4.3 Exponential Distribution Interval Estimation ..................................111
3.4.4 Lognormal Distribution....................................................................114
3.4.5 Weibull Distribution .........................................................................115
3.4.6 Binomial Distribution .......................................................................118
3.5 Classical Nonparametric Distribution Estimation .........................................119
3.5.1 Confidence Intervals for cdf and Reliability Function
for Complete and Singly Censored Data ..........................................119
3.5.2 Confidence Intervals for cdf and Reliability Function
for Multiply Censored Data ..............................................................123
3.6 Bayesian Estimation Procedures ...................................................................125
3.6.1 Estimation of the Parameter of Exponential Distribution ................127
3.6.1.1 Selecting Parameters of Prior Distribution .......................129
3.6.1.2 Uniform Prior Distribution ...............................................131
3.6.1.3 Jeffreys Prior Distribution ................................................133
3.6.2 Bayesian Estimation of the Parameter of Binomial Distribution .....133
3.6.2.1 Standard Uniform Prior Distribution ................................134
3.6.2.2 Truncated Standard Uniform Prior Distribution ..............135
3.6.2.3 Beta Prior Distribution .....................................................136
3.6.2.4 Jeffreys Prior Distribution for Parameter p of the
Binomial Distribution .......................................................140
3.6.2.5 Lognormal Prior Distribution ...........................................140
3.6.3 Bayesian Estimation of the Weibull Distribution .............................142
3.6.3.1 Prior Distribution ..............................................................143
3.6.3.2 Jeffreys Prior for Weibull Parameters .............................144
3.6.3.3 Posterior Distributions (Posterior Distribution
of Weibull cdf at a Fixed Exposure) .................................144
3.6.3.4 Posterior Distribution of Weibull Distribution
Parameters ........................................................................144
3.6.3.5 Particular Case ..................................................................148
3.6.4 Bayesian Probability Papers .............................................................149
3.6.4.1 Classical Simple Linear Regression .................................149
3.6.4.2 Classical Probability Papers .............................................152
3.6.4.3 Bayesian Simple Linear Regression and Bayesian
Probability Papers .............................................................153
3.6.4.4 Including Prior Information about Model Parameters .....153
3.6.4.5 Including Prior Information about the Reliability or cdf.....156
3.7 Methods of Generic Failure Rate Determination ..........................................158
References ................................................................................................................169
Chapter 4 System Reliability Analysis .....................................................................................173
4.1 Reliability Block Diagram Method ...............................................................173
4.1.1 Series System ...................................................................................173
viii Contents
4.1.2 Parallel Systems ...............................................................................175
4.1.3 Standby Redundant Systems ............................................................177
4.1.4 Load-Sharing Systems .....................................................................180
4.1.5 Complex Systems .............................................................................181
4.2 Fault Tree and Success Tree Methods ...........................................................185
4.2.1 Fault Tree Method ............................................................................185
4.2.2 Evaluation of Logic Trees ................................................................188
4.2.2.1 Analysis of Logic Trees Using Boolean Algebra .............188
4.2.2.2 Combinatorial (Truth Table) Technique for
Evaluation of Logic Trees .................................................193
4.2.2.3 Binary Decision Diagrams ...............................................196
4.2.3 Success Tree Method ........................................................................203
4.3 Event Tree Method ........................................................................................204
4.3.1 Construction of Event Trees .............................................................205
4.3.2 Evaluation of Event Trees .................................................................206
4.4 Master Logic Diagram ..................................................................................207
4.5 Failure Mode and Effect Analysis .................................................................214
4.5.1 Types of FMEA ................................................................................214
4.5.2 FMEA/FMECA Procedure ..............................................................215
4.5.3 FMEA Implementation ....................................................................215
4.5.3.1 FMEA for Aerospace Applications ..................................215
4.5.3.2 FMEA for Transportation Applications ...........................218
4.5.4 FMECA Procedure: Criticality Analysis .........................................226
References ................................................................................................................242
Chapter 5 Reliability and Availability of Repairable Components and Systems .....................243
5.1 Repairable System Reliability .......................................................................243
5.1.1 Basics of Point Processes .................................................................243
5.1.2 Homogeneous Poisson Process ........................................................246
5.1.3 Renewal Process ...............................................................................247
5.1.4 Nonhomogeneous Poisson Process ..................................................250
5.1.5 General Renewal Process .................................................................252
5.1.6 Probabilistic Bounds ........................................................................257
5.1.7 Nonparametric Data Analysis ..........................................................261
5.1.7.1 Estimation of the CIF .......................................................261
5.1.7.2 Estimation Based on One Realization
(Ungrouped Data) ............................................................261
5.1.7.3 Estimation Based on One Realization (Grouped Data) ......261
5.1.7.4 Estimation Based on Several Realizations .......................263
5.1.7.5 Confidence Limits for CIF ................................................263
5.1.8 Data Analysis for the HPP ...............................................................267
5.1.8.1 Procedures Based on the Poisson Distribution .................267
5.1.8.2 Procedures Based on the Exponential Distribution
of Time Intervals ..............................................................269
5.1.9 Data Analysis for the NHPP ............................................................270
5.1.9.1 Regression Analysis of Time Intervals .............................271
5.1.9.2 Maximum Likelihood Procedures ....................................273
5.1.9.3 Laplace’s Test ....................................................................275
5.1.10 Data Analysis for GRP .....................................................................278
5.1.10.1 Example Based on Simulated Data ..................................279
Contents ix
5.1.10.2 Example Based on Real Data ...........................................279
5.2 Availability of Repairable Systems ...............................................................280
5.2.1 Instantaneous (Point) Availability ....................................................281
5.2.2 Limiting Point Availability ..............................................................285
5.2.3 Average Availability .........................................................................285
5.2.4 Availability Measures Based on Causes of Unavailability ..............285
5.2.4.1 Inherent Availability .........................................................286
5.2.4.2 Achieved Availability .......................................................286
5.2.4.3 Operational Availability ...................................................286
5.3 Use of Markov Processes for Determining System Availability ...................286
5.4 Use of System Analysis Techniques in the Availability Calculations
of Complex Systems ......................................................................................292
References ................................................................................................................304
Chapter 6 Selected Topics in Reliability Modeling ..................................................................307
6.1 Probabilistic Physics-of-Failure Reliability Modeling ..................................307
6.1.1 Stress–Strength Model .....................................................................308
6.1.2 Damage–Endurance Model ..............................................................311
6.1.3 Performance–Requirement Model ...................................................317
6.2 Software Reliability Analysis ........................................................................318
6.2.1 Introduction ......................................................................................318
6.2.2 Software Reliability Models .............................................................319
6.2.2.1 Classification .....................................................................319
6.2.3 Software Life Cycle Models .............................................................323
6.2.3.1 Waterfall Model ................................................................324
6.3 Human Reliability .........................................................................................324
6.3.1 HRA Process ....................................................................................325
6.3.2 HRA Models ....................................................................................328
6.3.2.1 Simulation Methods ..........................................................328
6.3.2.2 Expert Judgment Methods ................................................329
6.3.2.3 Analytical Methods ..........................................................330
6.3.3 Human Reliability Data....................................................................334
6.4 Measures of Importance ................................................................................335
6.4.1 Birnbaum Measure of Importance ...................................................335
6.4.2 Criticality Importance ......................................................................336
6.4.3 Fussell–Vesely Importance...............................................................337
6.4.4 Risk-Reduction Importance .............................................................338
6.4.5 RAW Importance .............................................................................338
6.4.6 Practical Aspects of Importance Measures ......................................341
6.5 Maintenance Considerations in Reliability ...................................................342
6.5.1 Reliability-Centered Maintenance ...................................................342
6.5.2 Optimal Preventive Maintenance Scheduling ..................................345
6.5.2.1 Economic Benefit of Optimization ...................................346
6.5.3 Comparative Analysis of Optimal Maintenance Policies
under General Repair with Underlying Weibull Distributions ........346
6.6 Reliability Growth .........................................................................................348
6.6.1 Graphical Method ............................................................................348
6.6.2 Duane Method ..................................................................................348
6.6.3 Army Material Systems Analysis Activity Method .........................351
References ................................................................................................................356