Mathematical Theory of Reliability
Will be published approx. on 31. December 1996
Book
Paperback/Softback
273 pages
978-0-89871-369-5 (ISBN)
Description
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.
Mathematical reliability refers to a body of ideas, mathematical models, and methods directed toward the solution of problems in predicting, estimating, or optimizing the probability of survival, mean life, or, more generally, life distribution of components and systems. 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 republication. Mathematical Theory of Reliability now joins a growing list of volumes in SIAM's Classics series. Although contemporary reliability books are now available, few provide as mathematically rigorous a treatment of the required probability background as this one.
Mathematical reliability refers to a body of ideas, mathematical models, and methods directed toward the solution of problems in predicting, estimating, or optimizing the probability of survival, mean life, or, more generally, life distribution of components and systems. 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 republication. Mathematical Theory of Reliability now joins a growing list of volumes in SIAM's Classics series. Although contemporary reliability books are now available, few provide as mathematically rigorous a treatment of the required probability background as this one.
More details
Series
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Product notice
Paperback (trade)
Dimensions
Height: 228 mm
Width: 152 mm
Thickness: 14 mm
Weight
368 gr
ISBN-13
978-0-89871-369-5 (9780898713695)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Content
Preface to the Classics Edition
Preface
Acknowledgments
Chapter 1: Introduction. Historical Background of the Mathematical Theory of Reliability
Definitions of Reliability
Chapter 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
Chapter 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
Chapter 4: Optimum Maintenance Policies. Introduction
Replacement Policies
Inspection Policies
Chapter 5: Stochastic Models for Complex Systems. Introduction
Markov Chains and Semi-Markov Processes
Repairman Problems
Marginal Checking
Optimal Maintenance Policies under Markovian Deterioration
Chapter 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
Chapter 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.
Preface
Acknowledgments
Chapter 1: Introduction. Historical Background of the Mathematical Theory of Reliability
Definitions of Reliability
Chapter 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
Chapter 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
Chapter 4: Optimum Maintenance Policies. Introduction
Replacement Policies
Inspection Policies
Chapter 5: Stochastic Models for Complex Systems. Introduction
Markov Chains and Semi-Markov Processes
Repairman Problems
Marginal Checking
Optimal Maintenance Policies under Markovian Deterioration
Chapter 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
Chapter 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.