Stochastic Models in Reliability and Maintenance

Online-Ressource (XII, 338 p)

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1. Renewal Processes and Their Computational Aspects1.1 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 -- 6.3 g-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 of Application 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.

10.1007/978-3-540-24808-8 [DOI]

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