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Mathematical models for the study of the reliability of systems
Modèles mathématiques pour l'étude de la fiabilité des systèmes. English
1 online resource (x, 221 pages) : illustrations
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 Rate11 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 Networks23 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. Definitions32 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 2A.3 Relation to IFR Functions; Bibliography; Index
A. Kaufmann, D. Grouchko, R. Cruon ; translated by Technical Translations.
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL
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Includes bibliographical references (pages 215-217) and index.
Mathematics in science and engineering ; v. 124