Mathematical Models for the Study of the Reliability of Systems

Name: Mathematical Models for the Study of the Reliability of Systems
Brand: Academic Press
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Academic Press

Erschienen am 14. Mai 2014

233 Seiten

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978-0-08-095633-6 (ISBN)

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Front Cover
Mathematical Models for the Study of the Reliability of Systems
Copyright Page
Contents
Preface
List of Symbols
Chapter I. Lifetime of a Component
1 Introduction
2 Age and Lifetime of a Component
3 Survival Function
4 Failure Probability. Failure Rate
5 Moments of a Survival Law. Mean Failure Age
6 Principal Survival Laws Used in the Management of Equipment
7 Survival Law of Nonnew Equipment
8 Survival Law with Guarantee. Survival Law with a Limit on Functioning
Chapter II. Equipment with an Increasing Failure
9 Introduction
10 Survival Functions with Increasing (Decreasing) Failure Rate
11 Properties of IFR Functions
12 Survival Functions with Increasing Failure Rate Averages
Chapter III. Study of the Structure of Systems: Structure Functions and Reliability Networks
13 Introduction
14 Hypotheses on the Structure and Functioning of Systems
15 Structure Function
16 Links and Cuts
17 Mathematical Properties of Links and Cuts. Duality
18 Review of the Theory of Graphs
19 Reliability Networks
20 Equivalence between Structure Functions and Reliability Networks
21 Monotone (or Coherent) Structures
22 Construction and Simplification of Structure Functions and of Reliability Networks
23 Finding Links and Cuts
Chapter IV. Study of the Reliability of Systems
24 Introduction. Definitions and Hypotheses
25 The Reliability Function
26 Composition of Structures
27 Representative Curves of Reliability Functions for Monotone Structures. Theorem of Moore and Shannon
28 Systems Monotone in Probability
29 Survival Function of a System
30 Survival Functions for Series and Parallel Structures. Asymptotic Results for a Large Number of Components
Chapter V. Redundance
31 Introduction. Definitions
32 Active Redundance at the Level of Substructures or at the Level of Components
33 Optimal Redundance
34 Concavity of Monotone Structures with Respect to Redundance
35 Type k of n Structures
Chapter VI. Systems Presenting Two Dual Types of Failures
36 Introduction
37 Definition. Properties
38 Reliability Function of a System Presenting Two Types of Failures
39 Redundance in Systems with Components of the Same Reliabilities
40 Iterative Structures
Appendix Pólya Functions of Order 2. Totally Positive Functions of Order 2
A.1 Pólya Functions of Order 2
A.2 Totally Positive Functions of Order 2
A.3 Relation to IFR Functions
Bibliography
Index

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