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Statistical and Probabilistic Models in Reliability

Statistical and Probabilistic Models in Reliability

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Statistical and Probabilistic Models in Reliability

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Beschreibung

Details

Einband

Gebundene Ausgabe

Erscheinungsdatum

01.12.1998

Herausgeber

Nikolaos Limnios + weitere

Verlag

Birkhäuser Boston

Seitenzahl

352

Beschreibung

Details

Einband

Gebundene Ausgabe

Erscheinungsdatum

01.12.1998

Herausgeber

Verlag

Birkhäuser Boston

Seitenzahl

352

Maße (L/B/H)

26/18.3/2.6 cm

Gewicht

971 g

Auflage

1999

Sprache

Englisch

ISBN

978-0-8176-4068-2

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  • Statistical and Probabilistic Models in Reliability
  • I: Statistical Methods.- 1 Statistical Modeling and Analysis of Repairable Systems.- 1.1 Introduction.- 1.2 “Major Events” in the History of Repairable Systems Reliability.- 1.3 Notation and Basic Definitions.- 1.4 Classification of Repair Actions.- 1.5 The Trend-Renewal Process.- 1.6 Statistical Inference in Trend-Renewal Processes.- 1.7 Trend Testing.- 1.8 Monte Carlo Trend Tests.- 1.9 Concluding Remarks and Topics for Further Study.- References.- 2 CPIT Goodness-of-Fit Tests for Reliability Growth Models.- 2.1 Introduction.- 2.2 The Conditional Probabilty Integral Transformation.- 2.3 CPIT GOF Tests for the Homogeneous Poisson Process.- 2.4 CPIT GOF Tests for the Jelinski-Moranda and Goel-Okumoto Models.- 2.5 CPIT GOF Tests for the Power-Law Process.- 2.6 Experimental Results.- 2.7 Conclusion.- References.- 3 On the Use of Minimally Informative Copulae in Competing Risk Problems.- 3.1 Competing Risk.- 3.2 Bounds Without Assumptions on a Dependence Structure.- 3.2.1 Peterson bounds.- 3.2.2 Crowder-Bedford-Meilijson bounds.- 3.3 Estimators Using Dependence Assumptions.- 3.3.1 The copula-graphic estimator.- 3.4 Minimallly Informative Copulae.- 3.5 Examples.- 3.5.1 Example 1.- 3.5.2 Example 2.- 3.6 Conclusions.- References.- 4 Model Building in Accelerated Experiments.- 4.1 Introduction.- 4.2 Additive Accumulation of Damages Model and Its Submodels.- 4.3 Generalized Multiplicative Models.- 4.4 Generalized Additive and Additive-Multiplicative Models.- 4.5 Models Describing the Influence of Stresses to the Shape and Scale of Distribution.- 4.6 The Model of Sedyakin and Its Generalizations.- 4.7 The Heredity Hypothesis.- References.- 5 On Semiparametric Estimation of Reliability From Accelerated Life Data.- 5.1 Introduction.- 5.2 Estimation in the AAD Model.- 5.3 Properties of Estimators.- 5.4 Estimation, When Stresses Change the Shape of Distribution.- 5.5 Estimation in AFT Model, When G is Completely Unknown and r is Parametrized.- References.- 6 Analysis of Reliability Characteristics Estimators in Accelerated Life Testing.- 6.1 Introduction.- 6.2 Parametric Estimation.- 6.3 Nonparametric Estimation.- 6.4 Conclusion.- References.- 7 Chi-Squared Goodness of Fit Test for Doubly Censored Data With Applications in Survival Analysis and Reliability.- 7.1 Introduction.- 7.2 Weak Convergence of the Process Un(t).- 7.3 The Weak Convergence of the Process Un*(t).- 7.4 The Test Statistics.- References.- 8 Estimation of Kernel, Availability and Reliability of Semi-Markov Systems.- 8.1 Introduction.- 8.2 Estimator of the Semi-Markov Kernel.- 8.3 Estimation of the Markov Renewal Matrix and Its Asymptotic Properties.- 8.4 Estimation of the Semi-Markov Transition Matrix and Its Properties.- 8.5 Reliability and Availability Estimation.- 8.5.1 Availability.- 8.5.2 Reliability.- 8.5.3 Asymptotic properties of the estimators.- 8.6 Application.- References.- II: Probabilistic Methods.- 9 Stochastical Models of Systems in Reliability Problems.- 9.1 Introduction.- 9.2 Reliability Problem for a Redundant System.- 9.2.1 Repairable duplicated system.- 9.2.2 Sojourn time in a subset of states.- 9.3 Problems of Singular Perturbation.- 9.4 Analysis of Stochastic Systems.- 9.4.1 Phase merging scheme.- 9.4.2 Heuristic principles of phase merging.- 9.5 Diffusion Approximation Scheme.- References.- 10 Markovian Repairman Problems. Classification and Approximation.- 10.1 Introduction.- 10.2 Classification of Repairman Models.- 10.3 Asymptotical Analysis of Queueing Process.- References.- 11 On Limit Reliability Functions of Large Systems. Part I.- 11.1 Introduction.- 11.2 Limit Reliability Functions of Homogeneous Systems.- 11.3 Limit Reliability Functions of Nonhomogeneous Systems.- 11.4 Remarks on Limit Reliability Functions of Multi-State Systems.- 11.5 Summary.- References.- 12 On Limit Reliability Functions of Large Systems. Part II.- 12.1 Domains of Attraction of Limit Reliability Functions.- 12.2 Asymptotic Reliability Functions of a Regular Homogeneous Series-“k out of n” System.- 12.3 Limit Reliability Functions of Homogeneous Regular Series-Parallel Systems of Higher Order.- References.- 13 Error Bounds for a Stiff Markov Chain Approximation Technique and an Application.- 13.1 Introduction.- 13.2 Notations.- 13.3 Approximation Techniques.- 13.3.1 A path-based technique.- 13.3.2 Bobbio and Trivedi’s algorithm.- 13.4 Main Results.- 13.4.1 Equivalence.- 13.4.2 A non-conservative case.- 13.4.3 Error bounds.- 13.5 Numerical Example.- 13.5.1 Model used.- 13.5.2 Results.- 13.6 Conclusion.- A.1 Proof of Proposition 13.3.1.- A.2 Proof of Proposition 13.4.1.- A.3 Proof of Theorem 13.4.1.- References.- 14 On the Failure Rate of Components Subjected to a Diffuse Stress Environment.- 14.1 Introduction.- 14.2 The Mathematical Model.- 14.3 General Results.- 14.3.1 The case of a stress starting from a fixed level.- 14.3.2 The case of a stationary stress process.- 14.4 Particular Case of Interest.- 14.4.1 Instantaneous action of the stress.- 14.4.2 Cumulative action of the stress.- 14.5 A Shot-Noise Model With Diffuse Stress.- 14.6 Conclusion.- Appendix (Proof of Lemma 14.3.1).- References.- 15 Modelling the Reliability of a Complex System Under Stress Environment.- 15.1 Introduction.- 15.2 Modelling the Stress.- 15.3 System of n Identical Components Subjected to an Homogeneous Poisson Stress Process.- 15.4 Some Particular Configurations of the n Identical Component System.- 15.5 Architecture and Stress Influence.- 15.6 Example — System of Two Identical Components Subjected to a Common, Homogeneous Poisson Stress Process.- 15.7 Conclusions.- References.- 16 On the Failure Rate.- 16.1 Introduction.- 16.2 Failure Process.- 16.3 Semi-Markov Process.- References.- 17 Asymptotic Results for the Failure Time of Consecutive k-out-of-n Systems.- 17.1 Introduction.- 17.2 Strong Laws for the Failure Time of the System.- References.- III: Special Techniques and Applications.- 18 Two-State Start-Up Demonstration Testing.- 18.1 Introduction.- 18.2 Probability Generating Function.- 18.3 Probabilities and Recurrence Relations.- References.- 19 Optimal Prophylaxis Policy for Systems With Partly Observable Parameters.- 19.1 Introduction.- 19.2 One-Server System.- 19.2.1 Mathematical model.- 19.2.2 Coefficient of readiness.- 19.3 Two-Server System.- 19.3.1 Mathematical model.- 19.3.2 Coefficient of readiness.- 19.4 Optimization.- 19.4.1 Functional equation.- 19.4.2 Continuous semi-Markov process.- 19.4.3 Evaluation of functionals.- 19.4.4 Process of maximal values.- 19.4.5 Inversed Gamma-process.- References.- 20 Exact Methods to Compute Network Reliability.- 20.1 Introduction.- 20.2 Definitions and Notation.- 20.3 Enumeration.- 20.3.1 State enumeration.- 20.3.2 Path enumeration-Cut enumeration.- 20.4 Reduction With Factoring.- 20.5 Decomposition.- 20.5.1 The principle.- 20.5.2 Algorithm implementation.- 20.5.3 Complexity.- 20.5.4 Adaptation for other relability problems.- 20.6 Conclusion.- References.- 21 On Matroid Base Families and the Reliability Computation of Totally Amenable Systems.- 21.1 Preliminaries.- 21.2 Algorithmic Complexity of Reliability Computation and Domination Theory.- 21.3 Matroid Base Families.- 21.4 On the Complexity of Computing the Reliability of Matroid Base Family Systems.- 21.5 Conclusions.- References.- 22 The Computer-Assisted Analysis of the Semi-Markovian Stochastic Petri Nets and an Application.- 22.1 Introduction.- 22.2 Background Material in the Stochastic Behavior of Petri Nets.- 22.3 Computer-Assisted Analysis of the Semi-Markovian Petri Nets.- 22.4 Application.- 22.5 Conclusions.- References.- 23 Incremental Approach for Building Stochastic Petri Nets for Dependability Modeling.- 23.1 Introduction.- 23.2 Presentaiton of the Incremental Approach.- 23.3 Guidelines for Modular Construction of GSPN Models.- 23.4 Example: Duplex System.- 23.5 Conclusions.- References.- 24 Lifetime of High Temperature Working Pipes.- 24.1 Introduction.- 24.2 Failure Risk.- 24.3 Defining Reliability.- 24.4 Mathematical Model for Lifetime Estimations.- 24.5 Simulating Reliability.- 24.6 Algorithm of Simulation.- 24.7 Simulating Reliability for Components.- 24.8 Simulating System Reliability.- References.