Advances in Stochastic Models for Reliablity, Quality and Safety

Advances in Stochastic Models for Reliablity, Quality and Safety

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Advances in Stochastic Models for Reliablity, Quality and Safety

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Beschreibung

Details

Einband

Gebundene Ausgabe

Erscheinungsdatum

25.08.1998

Herausgeber

Jensen Kahle + weitere

Verlag

Birkhäuser Boston

Seitenzahl

382

Beschreibung

Details

Einband

Gebundene Ausgabe

Erscheinungsdatum

25.08.1998

Herausgeber

Verlag

Birkhäuser Boston

Seitenzahl

382

Maße (L/B/H)

26.1/18.6/2.6 cm

Gewicht

939 g

Auflage

1998 edition

Sprache

Englisch

ISBN

978-0-8176-4049-1

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  • Advances in Stochastic Models for Reliablity, Quality and Safety
  • I: Lifetime Analysis.- 1. The Generalized Linnik Distributions.- 1.1 Introductory Example and Preliminaries.- 1.2 Assembling Discrete Linnik and Discrete Stable Distributions.- 1.3 Calculation of Probabilities.- 1.4 Characterization via Survival Distributions.- 1.5 Asymptotic Behaviour.- References.- 2. Acceptance Regions and Their Application in Lifetime Estimation.- 2.1 Confidence Bounds Based on Acceptance Regions.- 2.1.1 Basic notations.- 2.1.2 Confidence bound and system of acceptance regions.- 2.1.3 The algorithm “System of lower ?-acceptance regions”.- 2.1.4 Quality of lower confidence bounds.- 2.1.5 Optimality of the algorithm.- 2.1.6 Quick determination vs. good quality.- 2.2 Confidence Bound for the Expectation of a Weibull Distribution.- 2.2.1 The model.- 2.2.2 Applying the algorithm “System of lower ?-acceptance regions”.- 2.2.3 Quality of lower confidence bounds for the expectation.- References.- 3. On Statistics in Failure-Repair Models Under Censoring.- 3.1 Introduction.- 3.2 Survival Data Analysis Under Censoring.- 3.3 Nonparametric Estimators for RT(t).- 3.4 The Failure-Repair Model Under Censoring.- 3.4.1 The general model.- 3.4.2 Model under Koziol-Green assumption.- References.- 4. Parameter Estimation in Renewal Processes with Imperfect Repair.- 4.1 Introduction.- 4.2 A General Model.- 4.3 Specifications.- 4.4 Parameter Estimation in the General Model.- 4.4.1 Estimation of the parameters of failure intensity.- 4.4.2 A simple model for estimating the degree of repair.- References.- 5. Investigation of Convergence Rates in Risk Theory in the Presence of Heavy Tails.- 5.1 A Model in Risk Theory.- 5.2 Limit Theorem.- 5.3 Rates of Convergence.- References.- 6. Least Squares and Minimum Distance Estimation in the Three-Parameter Weibull and Fréchet Models with Applications to River Drain Data.- 6.1 Introduction.- 6.2 Least Squares and Minimum Distance Methods.- 6.2.1 General.- 6.2.2 Least squares and minimum distance estimators for the three-parameter Weibull model.- 6.3 Modelling of River Drain Data.- 6.3.1 The data.- 6.3.2 General.- 6.3.3 Analysis of river Danube data.- 6.3.4 Analysis of river Main data.- References.- II: Reliability Analysis.- 7. Maximum Likelihood Estimation With Different Sequential k-out-of-n Systems.- 7.1 Introduction.- 7.2 Sequential k-out-of-n Systems With Unknown Model Parameters.- 7.3 Estimation in Specific Distributions.- 7.4 Sequential k-out-of-n Systems With Known Model Parameters and Underlying One-Parameter Exponential Family.- 7.5 Example: Sequential 2-out-of-4 System.- References.- 8. Stochastic Models for the Return of Used Devices.- 8.1 Introduction.- 8.2 Additive Models for Returns.- 8.3 Model Fit.- References.- 9. Some Remarks on Dependent Censoring in Complex Systems.- 9.1 Introduction and Summary.- 9.2 Dependence of the Components Within a Parallel System.- 9.2.1 Estimation of F by means of Fjk.- 9.2.2 Estimation of F by means of the Kaplan-Meier estimators of Fj.- 9.2.3 Estimation of F by means of multivariate Kaplan-Keier estimators.- 9.3 Dependence of the Lifelengths and their Censoring Variables.- References.- 10. Parameter Estimation in Damage Processes: Dependent Observations of Damage Increments and First Passage Time.- 10.1 Introduction.- 10.2 The Likelihood Function if Both Damage Increments and Failure Time are Observed.- 10.3 An Example.- 10.4 Appendix: Proof of Lemma 10.2.1.- References.- 11. Boundary Crossing Probabilities of Poisson Counting Processes with General Boundaries.- 11.1 Introduction.- 11.2 The Homogeneous Poisson Process.- 11.2.1 Upper boundary case.- 11.2.2 Lower boundary case.- 11.2.3 Two boundary case.- 11.3 The Nonhomogeneous Poisson Process.- 11.4 A Special Mixed Poisson Process.- References.- 12. Optimal Sequential Estimation for Markov-Additive Processes.- 12.1 Introduction.- 12.2 The Model and Sampling Times.- 12.3 Efficient Sequential Procedures.- 12.4 Minimax Sequential Procedures.- References.- 13. Some Models Describing Damage Processes and Resulting First Passage Times.- 13.1 Introduction.- 13.2 Basic Definitions.- 13.3 System Failure Time in the Case of Independent Marking.- 13.3.1 ML-Estimates for parameters in the distribution of the system failure time.- References.- 14. Absorption Probabilities of a Brownian Motion in a Triangular Domain.- 14.1 Introduction.- 14.2 A Random Walk Result and Some Used Limit Theorems.- 14.3 The Case of Equal Drifts.- 14.4 The Case of Opposite Drifts.- 14.5 Discussion of the Results.- References.- III: Network Analysis.- 15. A Simple Algorithm for Calculating Approximately the Reliability of Almost Arbitrary Large Networks.- 15.1 Introduction.- 15.2 Notations.- 15.3 The Approximation.- 15.3.1 Simple network.- 15.4 Algorithms.- 15.4.1 Compound system.- 15.5 Accuracy.- 15.5.1 Example 1: Network ARTI.- 15.5.2 Example 2: Network K6.- 15.5.3 Example 3: Network K7.- 15.5.4 Example 4: Network ALG.- 15.5.5 Example 5: LGR.- 15.5.6 Example 6: Network EVA.- 15.5.7 Example 7: Network DGN.- 15.5.8 Example 8: FNW.- 15.5.9 Example 9: Network TECL.- 15.5.10 Example 10: Network RCG.- 15.6 Conclusions.- References.- 16. Reliability Analysis of Flow Networks.- 16.1 Introduction.- 16.2 List of Used Symbols.- 16.3 Definitions.- 16.4 Flow Probability.- 16.5 Computation of the Flow Probability.- 16.5.1 The decomposition algorithm.- 16.5.2 Special values of the demanded flow.- 16.5.3 Special structures.- 16.5.4 Computation by a generating function.- References.- 17. Generalized Gram-Charlier Series A and C Approximation for Nonlinear Mechanical Systems.- 17.1 Introduction.- 17.2 Formulation of the Problem.- 17.3 Generalized Gram-Charlier-Series A Approximation.- 17.4 Generalized Gram-Charlier-Series C Approximation.- 17.5 Examples.- 17.6 Conclusions.- References.- 18. A Unified Approach to the Reliability of Recurrent Structures.- 18.1 Introduction.- 18.2 The Decomposition of a Graph.- 18.3 The All-Terminal Reliability of Recurrent Structures.- 18.4 Generalizations and Open Problems.- References.- IV: Process Control.- 19. Testing for the Existence of a Change-Point in a Specified Time Interval.- 19.1 Introduction.- 19.2 A Family of Tests.- 19.3 The Bootstrap-Test Family.- 19.4 The Proofs.- References.- 20. On the Integration of Statistical Process Control and Engineering Process Control in Discrete Manufacturing Processes.- 20.1 Introduction — Two Simple Examples.- 20.1.1 An example from statistical process control.- 20.1.2 An example from engineering process control.- 20.2 Comparison of SPC and EPC.- 20.2.1 History and range of application of SPC and EPC.- 20.2.2 Quality criteria in the parts and process industries.- 20.2.3 Technical properties of production processes in parts and process industries.- 20.2.4 Statistical tools of SPC and EPC.- 20.2.5 Process changes in SPC and EPC.- 20.2.6 Process monitoring in SPC and EPC.- 20.2.7 Actions on the production process in SPC and EPC.- 20.2.8 The structure of process models in SPC and EPC.- 20.3 Models of Process Changes in SPC and EPC.- 20.3.1 Process changes in SPC models.- 20.3.2 Process changes in EPC models.- 20.4 Process Control in SPC and EPC.- 20.4.1 Process control as process monitoring in SPC.- 20.4.2 Process control as process adjustment in EPC.- 20.5 Problems of the Integration of SPC and EPC.- 20.5.1 History of SPC/EPC integration.- 20.5.2 Models proposed in the literature for SPC/EPC integration.- 20.6 A General Model for the Integration of SPC and EPC.- 20.7 Special Models for the Integration of SPC and EPC.- 20.7.1 Additive disturbance and shift in drift parameter in the deterministic trend model.- 20.7.2 Additive disturbance and shift in drift parameter in the random walk with drift model.- 20.8 Discussion of SPC in the Presence of EPC.- 20.8.1 Effect of simple shifts on EPC controlled processes.- 20.8.2 Shifts occurring during production time.- 20.8.3 Effect of a biased drift parameter estimate.- 20.8.4 Effect of constraints in the compensatory variable.- 20.8.5 Effect of using a wrong model.- 20.9 Conclusion.- References.- 21. Controlling a Process with Three Different States.- 21.1 Introduction.- 21.2 Process Model.- 21.3 Control Model.- 21.4 Long Run Profit Per Item.- 21.5 Renewal-Strategy.- 21.6 Inspection-Strategy.- 21.7 Adjustment-Strategy.- 21.8 Numerical Examples.- References.- 22. CUSUM Schemes and Erlang Distributions.- 22.1 Introduction.- 22.2 Transition Kernel and Integral Equations.- 22.3 Solution of the Integral Equations.- 22.4 Numerical Example.- 22.5 Conclusions.- References.- 23. On the Average Delay of Control Schemes.- 23.1 Introduction.- 23.2 On the Average Delay of a Generalized Shewhart Chart.- 23.2.1 Bounds for the average delay.- 23.2.2 The average delay for exchangeable variables.- 23.3 A Comparison of Several Control Charts.- 23.4 Conclusions.- References.- 24. Tolerance Bounds and Cpk Confidence Bounds Under Batch Effects.- 24.1 Introduction and Overview.- 24.2 Effective Sample Size and its Estimation.- 24.3 Tolerance Bounds.- 24.3.1 No between batch variation.- 24.3.2 No within batch variation.- 24.3.3 The interpolation step.- 24.4 Confidence Bounds for CL, CU and Cpk.- 24.4.1 No between batch variation.- 24.4.2 No within batch variation.- 24.4.3 The interpolation step.- 24.5 Validation.- 24.6 Sample Calculation.- 24.7 Concluding Remarks.- References.