## Table of contents for Mathematical theory of reliability / Richard E. Barlow, Frank Proschan with contributions by Larry C. Hunter.

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Preface to the Classics Edition; Preface; 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

Library of Congress subject headings for this publication:

Reliability (Engineering) -- Mathematical models.

Mathematical statistics.

Probabilities.