Mathematical Theory of Reliability

Table of Contents

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.