Mathematical Models for the Study of the Reliability of Systems

Description

Front Cover 2
Mathematical Models for the Study of the Reliability of Systems 5
Copyright Page 6
Contents 7
Preface 9
List of Symbols 11
Chapter I. Lifetime of a Component 13
- 1 Introduction 13
- 2 Age and Lifetime of a Component 14
- 3 Survival Function 18
- 4 Failure Probability. Failure Rate 21
- 5 Moments of a Survival Law. Mean Failure Age 25
- 6 Principal Survival Laws Used in the Management of Equipment 28
- 7 Survival Law of Nonnew Equipment 40
- 8 Survival Law with Guarantee. Survival Law with a Limit on Functioning 41

Front Cover 2
Mathematical Models for the Study of the Reliability of Systems 5
Copyright Page 6
Contents 7
Preface 9
List of Symbols 11
Chapter I. Lifetime of a Component 13
- 1 Introduction 13
- 2 Age and Lifetime of a Component 14
- 3 Survival Function 18
- 4 Failure Probability. Failure Rate 21
- 5 Moments of a Survival Law. Mean Failure Age 25
- 6 Principal Survival Laws Used in the Management of Equipment 28
- 7 Survival Law of Nonnew Equipment 40
- 8 Survival Law with Guarantee. Survival Law with a Limit on Functioning 41
Chapter II. Equipment with an Increasing Failure 45
- 9 Introduction 45
- 10 Survival Functions with Increasing (Decreasing) Failure Rate 46
- 11 Properties of IFR Functions 52
- 12 Survival Functions with Increasing Failure Rate Averages 58
Chapter III. Study of the Structure of Systems: Structure Functions and Reliability Networks 67
- 13 Introduction 67
- 14 Hypotheses on the Structure and Functioning of Systems 68
- 15 Structure Function 68
- 16 Links and Cuts 73
- 17 Mathematical Properties of Links and Cuts. Duality 77
- 18 Review of the Theory of Graphs 80
- 19 Reliability Networks 83
- 20 Equivalence between Structure Functions and Reliability Networks 92
- 21 Monotone (or Coherent) Structures 95
- 22 Construction and Simplification of Structure Functions and of Reliability Networks 104
- 23 Finding Links and Cuts 111
Chapter IV. Study of the Reliability of Systems 126
- 24 Introduction. Definitions and Hypotheses 126
- 25 The Reliability Function 128
- 26 Composition of Structures 135
- 27 Representative Curves of Reliability Functions for Monotone Structures. Theorem of Moore and Shannon 147
- 28 Systems Monotone in Probability 152
- 29 Survival Function of a System 158
- 30 Survival Functions for Series and Parallel Structures. Asymptotic Results for a Large Number of Components 171
Chapter V. Redundance 179
- 31 Introduction. Definitions 179
- 32 Active Redundance at the Level of Substructures or at the Level of Components 181
- 33 Optimal Redundance 184
- 34 Concavity of Monotone Structures with Respect to Redundance 192
- 35 Type k of n Structures 195
Chapter VI. Systems Presenting Two Dual Types of Failures 202
- 36 Introduction 202
- 37 Definition. Properties 204
- 38 Reliability Function of a System Presenting Two Types of Failures 206
- 39 Redundance in Systems with Components of the Same Reliabilities 210
- 40 Iterative Structures 215
Appendix Pólya Functions of Order 2. Totally Positive Functions of Order 2 219
- A.1 Pólya Functions of Order 2 219
- A.2 Totally Positive Functions of Order 2 224
- A.3 Relation to IFR Functions 225
Bibliography 227
Index 231

Description

TOC

Reviews (0)