Mathematical Theory of Reliability

Erscheinungsjahr 1987
ISBN: 978-0-89871-369-5
Verlag: CAMBRIDGE UNIVERSITY PRESS

Buch, Englisch, Band 17, 274 Seiten, Format (B × H): 154 mm x 229 mm, Gewicht: 388 g

Reihe: Classics in Applied Mathematics

This monograph presents a survey of mathematical models useful in solving reliability problems. It includes a detailed discussion of life distributions corresponding to wearout and their use in determining maintenance policies, and covers important topics such as the theory of increasing (decreasing) failure rate distributions, optimum maintenance policies, and the theory of coherent systems. The emphasis throughout the book is on making minimal assumptions - and only those based on plausible physical considerations - so that the resulting mathematical deductions may be safely made about a large variety of commonly occurring reliability situations. The first part of the book is concerned with component reliability, while the second part covers system reliability, including problems that are as important today as they were in the 1960s. The enduring relevance of the subject of reliability and the continuing demand for a graduate-level book on this topic are the driving forces behind its re-publication.

Autoren/Hrsg.

Barlow, Richard E.

Proschan, Frank

Fachgebiete

• Mathematik | Informatik Mathematik Operations Research
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

Preface to the Classics Edition
Preface
1. Introduction. Historical Background of the Mathematical Theory of Reliability
Definitions of Reliability
2. Failure Distributions. Introduction
Typical Failure Laws
The Exponential as the Failure Law of Complex Equipment
Monotone Failure Rates
Preservation of Monotone Failure Rate
Additional Inequalities
General Failure Rates
3. Operating Characteristics of Maintenance Policies. Introduction
Renewal Theory
Replacement Based on Age
Comparison of Age and Block Replacement Policies
Random Replacement
Repair of a Single Unit
4. Optimum Maintenance Policies. Introduction
Replacement Policies
Inspection Policies
5. Stochastic Models for Complex Systems. Introduction
Markov Chains and Semi-Markov Processes
Repairman Problems
Marginal Checking
Optimal Maintenance Policies under Markovian Deterioration
6. Redundancy Optimization. Introduction
Optimal Allocation of Redundancy Subject to Constraints
Application to Parallel Redundancy Model
Application to Standby Redundancy Model
Complete Families of Undominated Allocations
Optimal Redundancy Assuming Two Types of Failure
7. Qualitative Relationships for Multicomponent Structures. Introduction
Achieving Reliable Relay Circuits
Monotonic Structures
S-shaped Reliability Functions for Monotonic Structures
k-out-of-n Structures
Relationship between Structures Failure Rate and Component Failure Rates
Appendix 1. Total Positivity
Appendix 2. Test for Increasing Failure Rate
Appendix 3. Tables Giving Bounds on Distributions with Monotone Failure Rate
References
Index.