Stochastic Models in Reliability and Maintenance (Hardcover)

1. Renewal Processes and Their Computational Aspects.- 1.1 Introduction.- 1.2 Basic Renewal Theory.- 1.2.1 Continuous renewal theory.- 1.2.2 Discrete renewal theory.- 1.3 Some Useful Properties of the Renewal Function.- 1.3.1 Specific examples.- 1.3.2 Asymptotic properties.- 1.4 Analytical Approximation Methods.- 1.4.1 Phase renewal processes.- 1.4.2 Gamma approximations.- 1.4.3 Methods based on equilibrium distribution.- 1.5 Bounds.- 1.6 Numerical Methods.- 1.6.1 Laplace inversion technique.- 1.6.2 Cubic spline algorithm.- 1.6.3 Discritization algorithm.- 1.6.4 Approximation by rational functions.- 1.7 Concluding Remarks.- 2. Stochastic Orders in Reliability Theory.- 2.1 Introduction.- 2.2 Definitions and Basic Properties.- 2.2.1 Stochastic orders generated from univariate functions.- 2.2.2 Conditional stochastic orders.- 2.2.3 Bivariate characterization of stochastic orders.- 2.3 Applications in Reliability Theory.- 2.3.1 Notions of aging.- 2.3.2 Useful stochastic inequalities in reliability theory.- 2.3.3 Stochastic comparisons of system reliabilities.- 2.3.4 Redundancy improvement.- 2.3.5 Stochastic comparisons of maintenance policies.- 2.3.5.1 Replacements upon failures.- 2.3.5.2 Age replacement.- 2.3.5.3 Block replacement.- 2.3.5.4 Minimal repair.- 2.3.5.5 Minimal repair with block replacement.- 2.3.5.6 Stochastic comparison of different maintenance policies.- 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.- 5.2.1 Introduction.- 5.2.2 Model A - age.- 5.2.3 Model B - failure rate.- 5.2.4 Numerical examples.- 5.3 Shock Model with Imperfect Preventive Maintenance.- 5.3.1 Introduction.- 5.3.2 Model and expected cost.- 5.3.3 Optimal policies.- 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.- 7.2.1 Model and assumptions.- 7.2.2 First-passage time distributions.- 7.2.3 Expected numbers of visits to state.- 7.2.4 Transition probabilities.- 7.3 Preventive Maintenance of Two-Unit Systems.- 7.3.1 Model and analysis.- 7.3.2 Optimum preventive maintenance policies.- 7.3.3 Replacement of a two-unit parallel system.- 7.4 Other Two-Unit Systems.- 7.4.1 Two-unit parallel system.- 7.4.2 Two-unit priority standby system.- 7.4.3 Two-unit standby system with imperfect switchover.- 7.4.4 Other models.- 8. Optimal Maintenance Problems for Markovian Deteriorating Systems.- 8.1 A Basic Optimal Replacement Problem for a Discrete Time Markovian Deteriorating System.- 8.1.1 Some conditions on transition probabilities and cost structure.- 8.1.2 Formulation by Markovian decision process