Mathematical Theory of Reliability

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.