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.
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