Mathematical Theory of Reliability

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.