Binary Decision Diagrams and Extensions for System Reliability Analysis

238 Pages·2015·2.89 MB·English

by  Amari

Binary Decision Diagrams and
Extensions for System Reliability
Analysis
Scrivener Publishing
100 Cummings Center, Suite 541J
Beverly, MA 01915-6106
Performability Engineering Series
Series Editors: Krishna B. Misra ([email protected])
and John Andrews ([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 mini-
mizing 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 indica-
tive of achieving quality, reliability, maintainability and safety for a product, sys-
tem, 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 activ-
ity in creating a product, system, or service is always associated with certain envi-
ronmental impacts that follow at each phase of development. These considerations
have become all the more necessary in the 21st century as the world resources con-
tinue 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 economi-
cally viable and safe processes (clean production and clean technologies), we will
create minimal adverse effect on the environment during production and dis-
posal 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 objec-
tive to help create optimal and sustainable products, systems, and services.
Publishers at Scrivener
Martin Scrivener([email protected])
Phillip Carmical ([email protected])
Binary Decision
Diagrams and
Extensions for System
Reliability Analysis
Liudong Xing and Suprasad V. Amari
Copyright © 2015 by Scrivener Publishing LLC. All rights reserved.
Co-published by John Wiley & Sons, Inc. Hoboken, New Jersey, and Scrivener Publishing LLC, Salem,
Massachusetts.
Published simultaneously in Canada.
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Cover design by Russell Richardson
Library of Congr ess Cataloging-in-Publication Data:
ISBN 978-1-118-54937-7
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
To Kevin X. Zhang
and
Joseph Amari

Contents
Preface xiii
Nomenclature xix
1 Introduction 1
1.1 Historical Developments 1
1.2 Reliability and Safety Applications 4
2 Basic Reliability Theory and Models 7
2.1 Probabiltiy Concepts 7
2.1.1 Axioms of Probability 8
2.1.2 Total Probability Law 9
2.1.3 Random Variables 10
2.1.4 Parameters of Random Variables 11
2.1.5 Lifetime Distributions 12
2.2 Reliability Measures 14
2.2.1 Time-to-Failure and Failure Function 14
2.2.2 Reliability Function 14
2.2.3 Failure Rate Function 15
2.2.4 Mean Time to Failure 16
2.2.5 Mean Residual Life 17
2.3 Fault Tree Analysis 17
2.3.1 Overview 17
2.3.2 Fault Tree Construction 18
2.3.3 Different Forms of Fault Trees 21
2.3.3.1 Static Fault Trees 21
2.3.3.2 Dynamic Fault Trees (DFTs) 22
2.3.3.3 Noncoherent Fault Trees 24
vii
viii Contents
2.3.4 Types of Fault Tree Analysis 24
2.3.4.1 Qualitative Analysis 25
2.3.4.2 Quantitative Analysis 27
2.3.5 Fault Tree Analysis Techniques 28
2.3.5.1 Inclusion-Exclusion (I-E) 28
2.3.5.2 Sum of Disjoint Products (SDPs) 30
3 Fundamentals of Binary Decision Diagrams 33
3.1 Preliminaries 34
3.2 Basic Concepts 34
3.3 BDD Construction 35
3.3.1 Input Variable Ordering 35
3.3.2 OBDD Generation 37
3.3.3 ROBDD Generation 38
3.3.4 Example Illustrations 39
3.4 BDD Evaluation 42
3.5 BDD-Based Software Package 44
4 Application of BDD to Binary-State Systems 45
4.1 Network Reliability Analysis 45
4.2 Event Tree Analysis 47
4.3 Failure Frequency Analysis 50
4.3.1 Steady-State System Failure Frequency 51
4.3.2 Time-Dependent System Failure and
Success Frequencies 53
4.4 Importance Measures and Analysis 54
4.4.1 Deterministic Importance Measures 54
4.4.2 Probabilistic Importance Measures 56
4.4.2.1 Birnbaum’s Measure 56
4.4.2.2 Criticality Importance Factor 58
4.4.2.3 Fussell-Vesely Measure 59
4.5 Modularization Methods 60
4.6 Non-Coherent Systems 60
4.6.1 Prime Implicants Based Method 61
4.6.2 BDD Based Method 64
4.7 Disjoint Failures 65
4.8 Dependent Failures 68
4.8.1 Common-Cause Failures (CCFs) 68
4.8.2 Functional Dependent Failures 71