Stochastic Models in Reliability and Maintenance

Our daily lives can be maintained by the high-technology systems. Computer systems are typical examples of such systems. We can enjoy our modern lives by using many computer systems. Much more importantly, we have to maintain such systems without failure, but cannot predict when such systems will fail and how to fix such systems without delay. A stochastic process is a set of outcomes of a random experiment indexed by time, and is one of the key tools needed to analyze the future behavior quantitatively. Reliability and maintainability technologies are of great interest and importance to the maintenance of such systems. Many mathematical models have been and will be proposed to describe reliability and maintainability systems by using the stochastic processes. The theme of this book is "Stochastic Models in Reliability and Main tainability. " This book consists of 12 chapters on the theme above from the different viewpoints of stochastic modeling. Chapter 1 is devoted to "Renewal Processes," under which classical renewal theory is surveyed and computa tional methods are described. Chapter 2 discusses "Stochastic Orders," and in it some definitions and concepts on stochastic orders are described and ag ing properties can be characterized by stochastic orders. Chapter 3 is devoted to "Classical Maintenance Models," under which the so-called age, block and other replacement models are surveyed. Chapter 4 discusses "Modeling Plant Maintenance," describing how maintenance practice can be carried out for plant maintenance.

1. Renewal Processes and Their Computational Aspects.- 1.1 Introduction.- 1.2 Basic Renewal Theory.- 1.3 Some Useful Properties of the Renewal Function.- 1.4 Analytical Approximation Methods.- 1.5 Bounds.- 1.6 Numerical Methods.- 1.7 Concluding Remarks.- 2. Stochastic Orders in Reliability Theory.- 2.1 Introduction.- 2.2 Definitions and Basic Properties.- 2.3 Applications in Reliability Theory.- 2.A TP2 Functions.- 3. Classical Maintenance Models.- 3.1 Introduction.- 3.2 Block Replacement.- 3.3 Age Replacement.- 3.4 Order Replacement.- 3.5 Inspection Strategies.- 3.6 Conclusions.- 4. A Review of Delay Time Analysis for Modelling Plant Maintenance.- 4.1 Introduction.- 4.2 Maintenance Practice.- 4.3 The Delay Time Concept.- 4.4 Basic Delay Time Maintenance Model: Complex Plant.- 4.5 Basic Maintenance Model: Component Tracking.- 4.6 Relaxation of Assumptions.- 4.7 Non-perfect Inspection.- 4.8 Non-steady-state Condition.- 4.9 Non-homogeneous Defect Arrival Rate ?.- 4.10 Condition-dependent Cost and Downtime for Repair.- 4.11 Case Experience Using Subjective Data: Case Experience.- 4.12 Revision of Subjectively Estimated Delay Time Distribution.- 4.13 Correction for Sampling Bias.- 4.14 Subjective Estimation of the Delay Time Distribution Directly.- 4.15 Objective Estimation of Delay Time Parameters.- 4.16 Case Experience Using Objective Data: HPP of Defect Arrival.- 4.17 Discussion of Further Developments in Delay Time Modelling.- 4.18 Conclusions.- 5. Imperfect Preventive Maintenance Models.- 5.1 Introduction.- 5.2 Sequential Imperfect Preventive Maintenance.- 5.3 Shock Model with Imperfect Preventive Maintenance.- 5.4 Conclusions.- 6. Generalized Renewal Processes and General Repair Models.- 6.1 Background and Motivation.- 6.2 Generalized Renewal Processes.- 6.3g-Renewal Processes in Discrete Time.- 6.4 Monotonicity and Asymptotic Properties of the g-Renewal Density.- 6.5 On the g-Renewal Function.- 6.6 A General Repair Model.- 7. Two-Unit Redundant Models.- 7.1 Introduction.- 7.2 Two-Unit Standby System.- 7.3 Preventive Maintenance of Two-Unit Systems.- 7.4 Other Two-Unit Systems.- 8. Optimal Maintenance Problems for Markovian Deteriorating Systems.- 8.1 A Basic Optimal Replacement Problem for a Discrete Time Markovian Deteriorating System.- 8.2 An Optimal Inspection and Replacement Problem.- 8.3 An Optimal Inspection and Replacement Policy with Incomplete Information.- 8.4 A Continuous Time Markovian Deteriorating System.- 8.5 An Optimal Maintenance Problem for a Queueing System.- 9. Transient Analysis of Semi-Markov Reliability Models - A Tutorial Review with Emphasis on Discrete-Parameter Approaches.- 9.1 Introduction.- 9.2 Modelling Framework.- 9.3 Dependability Measures.- 9.4 Methods of Analysis.- 9.5 Equations for the Dependability Measures.- 9.6 Numerical Solution Techniques.- 9.7 Recent Developments, Conclusions and Further Work.- 10. Software Reliability Models.- 10.1 Introduction.- 10.2 Definitions and Software Reliability Model.- 10.3 Software Reliability Growth Modeling.- 10.4 Imperfect Debugging Modeling.- 10.5 Software Availability Modeling.- 10.6 Application of Software Reliability Assessment.- 11. Reliability Models in Data Communication Systems.- 11.1 Introduction.- 11.2 SW ARQ Model with Intermittent Faults.- 11.3 SR ARQ Model with Retransmission Number.- 11.4 Hybrid ARQ Models with Response Time.- 12. Quick Monte Carlo Methods in Stochastic Systems and Reliability.- 12.1 Introduction.- 12.2 The Problem with Direct Simulation.- 12.3 Importance Sampling.- 12.4 The Optimal Change of Measure.- 12.5 Cases ofApplication of the Recursive Approach.- 12.6 System Model.- 12.7 Regenerative Simulation.- 12.8 Failure Biasing Methods.- 12.9 Unreliability Estimation.- 12.10 Analytical-Statistical Methods.- 12.11 Concluding Remarks.