Stochastic Models in Reliability and Maintenance - neues Buch

EAN (ISBN-13): 9783540248088
Erscheinungsjahr: 2012
Herausgeber: Springer Berlin Heidelberg

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ISBN/EAN: 9783540248088

ISBN - alternative Schreibweisen:
978-3-540-24808-8
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Autor des Buches: springer louis
Titel des Buches: stochastic models

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Daten vom Verlag:

Autor/in: Shunji Osaki
Titel: Stochastic Models in Reliability and Maintenance
Verlag: Springer; Springer Berlin
338 Seiten
Erscheinungsjahr: 2012-11-02
Berlin; Heidelberg; DE
Gedruckt / Hergestellt in Deutschland.
Sprache: Englisch
96,29 € (DE)
99,00 € (AT)
118,00 CHF (CH)
Available
XII, 338 p.

EA; E107; eBook; Nonbooks, PBS / Mathematik/Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik; Wahrscheinlichkeitsrechnung und Statistik; Verstehen; Markov; Markov process; Simulation; Stochastic models; calculus; communication; maintenance; model; modeling; numerical methods; optimization; reliability; renewal theory; statistical method; stochastic systems; C; Probability Theory and Stochastic Processes; Operations Research/Decision Theory; Industrial and Production Engineering; Probability Theory; Operations Research and Decision Theory; Industrial and Production Engineering; Mathematics and Statistics; Stochastik; Unternehmensforschung; Management: Entscheidungstheorie; Fertigungstechnik und Ingenieurwesen; BB

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 (MDP).- 8.1.3 Optimality of control limit rule.- 8.2 An Optimal Inspection and Replacement Problem.- 8.2.1 Transition probability.- 8.2.2 Formulation by semi-Markov decision process (SMDP).- 8.2.3 Structure of optimal inspection and replacement policy.- 8.3 An Optimal Inspection and Replacement Policy with Incomplete Information.- 8.3.1 Some notations and conditions.- 8.3.2 Formulation by partially observable Markov decision process (POMDP).- 8.3.3 Some properties of TP2 order.- 8.3.4 Some properties of optimal function.- 8.3.5 Structure of optimal inspection and replacement policy.- 8.4 A Continuous Time Markovian Deteriorating System.- 8.4.1 A continuous time Markovian deteriorating system.- 8.4.2 Transition probability.- 8.4.3 Formulation by semi-Markov decision process.- 8.4.4 Structure of optimal policy.- 8.5 An Optimal Maintenance Problem for a Queueing System.- 8.5.1 Model description.- 8.5.2 Formulation by semi-Markov decision process.- 8.5.3 Properties of value function.- 8.5.4 Structure of optimal policy.- 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.- 9.4.1 Continuous-parameter models.- 9.4.2 Discrete-parameter models.- 9.5 Equations for the Dependability Measures.- 9.6 Numerical Solution Techniques.- 9.6.1 Solving the integral equations.- 9.6.2 Discrete-parameter approximations.- 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.- 10.4.1 Imperfect debugging model with perfect correction rate.- 10.4.2 Imperfect debugging model for introduced faults.- 10.5 Software Availability Modeling.- 10.5.1 Model description.- 10.5.2 Software availability measures.- 10.6 Application of Software Reliability Assessment.- 10.6.1 Optimal software release problem.- 10.6.1.1 Maintenance cost model.- 10.6.1.2 Maintenance cost model with reliability requirement.- 10.6.2 Statistical software testing-progress control.- 10.6.3 Optimal testing-effort allocation problem.- 11. Reliability Models in Data Communication Systems.- 11.1 Introduction.- 11.2 SW ARQ Model with Intermittent Faults.- 11.2.1 Intermittent faults.- 11.2.2 ARQ policy.- 11.2.3 Optimal retransmission number.- 11.2.4 Numerical examples and remarks.- 11.3 SR ARQ Model with Retransmission Number.- 11.3.1 Model and analysis.- 11.3.2 Optimal policy.- 11.3.3 Numerical examples and remarks.- 11.4 Hybrid ARQ Models with Response Time.- 11.4.1 Type-I hybrid ARQ.- 11.4.2 Type-II hybrid ARQ.- 11.4.3 Comparison of type-I and type-II hybrid ARQs.- 11.4.4 Numerical examples and remarks.- 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.- 12.4.1 Remarks.- 12.4.2 Preliminary definitions.- 12.4.3 The recursive approach.- 12.4.4 Exact calculation of ?(x).- 12.5 Cases of Application of the Recursive Approach.- 12.6 System Model.- 12.7 Regenerative Simulation.- 12.8 Failure Biasing Methods.- 12.8.1 Simple failure biasing (SFB).- 12.8.2 Balanced failure biasing (BFB).- 12.8.3 Bias2 failure biasing.- 12.8.4 Failure distance biasing (FDB).- 12.8.5 Balanced 1 failure biasing (B1FB).- 12.8.6 Balanced 2 failure biasing (B2FB).- 12.8.7 Bounded relative error and failure biasing.- 12.9 Unreliability Estimation.- 12.9.1 One-component system.- 12.9.2 General case.- 12.9.3 Example.- 12.10 Analytical-Statistical Methods.- 12.11 Concluding Remarks.