Advances in Reliability: Balakrishnan, N.: 9780444500786: Book: Technology: eCampus.com

Preface

Contributors

xix

PART I. RELIABILITY MODELS

Basic Probabilistic Models in Reliability

(42)

N. Balakrishnan

N. Limnios

C. Papadopoulos

Introduction

(1)

Discrete time Markov chains and reliability

(8)

Continuous time Markov chains and reliability

(4)

Semi-Markov processes and reliability

(6)

Monte Carlo methods in reliability

(4)

Variance reduction methods

(11)

Simulation for semi-Markov systems

(7)

References

(3)

The Weibull Nonhomogeneous Poisson Process

(26)

Asit P. Basu

Steven E. Rigdon

The Poisson processes

(2)

Models for the reliability of repairable systems

(1)

Some data sets

(3)

Point and interval estimation for the power law process

(8)

Goodness-of-fit tests

(1)

Estimation of the intensity function

(2)

Multiple systems modeled with the power law process

(6)

An extension of the power law process

(3)

References

(1)

PART II. LIFE DISTRIBUTIONS

Bathtub-Shaped Failure Rate Life Distributions

(36)

C. D. Lai

M. Xie

D. N. P. Murthy

Introduction

(1)

Notions of aging

(2)

Bathtub-shaped failure rate life distributions

(4)

Families of bathtub-shaped failure rate distributions

(5)

Construction techniques for BFR distributions

(2)

Tests of exponentiality versus bathtub distribution

(2)

Change point estimations for BFR distributions

(1)

Applications

(2)

Mean residual life and bathtub shaped life distributions

(3)

Optimal burn-in-time for bathtub distributions

(4)

Models extending the traditional BFR distributions

(10)

References

(6)

Equilibrium Distribution - its Role in Reliability Theory

105

(34)

A. Chatterjee

S. P. Mukherjee

Introdution

105

(1)

History and genesis

106

(1)

Equilibrium distributions and dominance relations

107

(1)

Equilibrium distributions of higher orders: Properties and generalized order relations

108

(6)

Closure of generalized order relations

114

(10)

Equilibrium distribution in higher dimension

124

(7)

Equilibrium distribution in the context of repairable systems

131

(3)

Characterization of exponential distribution

134

(1)

Concluding remarks

135

(4)

Acknowledgment

135

(1)

References

135

(4)

PART III. RELIABILITY PROPERTIES

Reliability and Hazard Based on Finite Mixture Models

139

(46)

Essam K. AL-Hussaini

Khalaf S. Sultan

Introduction

139

(3)

Concepts, notation and definitions

142

(5)

Models with components belonging to the same family

147

(18)

Models with components belonging to different families

165

(11)

Summary and remarks

176

(9)

References

177

(8)

Mixtures and Monotonicity of Failure Rate Functions

185

(14)

Moshe Shakes

Fabio Spizzichino

Introduction

185

(1)

Monotonicity of the hazard rate of a mixture

186

(5)

Limiting behavior of the hazard rate of a mixture

191

(2)

Negative aging properties of multivariate exchangeable mixtures

193

(1)

Some results on univariate scale mixtures

194

(5)

References

197

(2)

Hazard Measure and Mean Residual Life Orderings: A Unified Approach

199

(16)

Majid Asadi

D. N. Shanbhag

Introduction

199

(1)

Some basic definitions and auxiliary results

200

(3)

Hazard measure ordering and its relationships with other partial orderings

203

(3)

Some closure properties of the hazard measure ordering

206

(9)

References

214

(1)

Some Comparison Results of the Reliability Functions of Some Coherent Systems

215

(12)

Jie Mi

Introduction

215

(1)

Main result

216

(4)

Applications

220

(7)

References

225

(2)

On the Reliability of Hierarchical Structures

227

(10)

Lev B. Klebanov

Gabor J. Szekely

Introduction

227

(1)

The main equation and its analytic solutions

228

(3)

The general solution of the main equation

231

(2)

Other normalizations

233

(1)

Reconstruction of the reliability polynomial from the limit distribution

233

(1)

A generalization of the main equation

234

(1)

A General limit result

235

(2)

References

235

(2)

PART IV. RELIABILITY SYSTEMS

Consecutive k-out-of-n Systems

237

(44)

N. A. Mokhlis

Introduction

238

(3)

Exact reliability formulas

241

(23)

Approximation formulas and bounds

264

(17)

References

279

(2)

Exact Reliability and Lifetime of Consecutive Systems

281

(20)

Sigeo Aki

Introduction

281

(2)

Reliability of consecutive systems of directed trees

283

(3)

Algorithms for exact reliability and numerical examples

286

(6)

Lifetime of consecutive systems

292

(9)

References

298

(3)

Sequential k-out-of-n Systems

301

(72)

E. Cramer

U. Kamps

Introduction

302

(7)

Sequential order statistics

309

(8)

Sampling situation

317

(1)

Maximum likelihood estimators of model parameters for arbitrary distributions

317

(3)

Test procedures for model selection

320

(5)

A location-scale family of distributions

325

(9)

Joint maximum likelihood estimation of model and distribution parameters

334

(3)

Estimation of the scale parameter

337

(8)

Joint estimation of location and scale parameters

345

(6)

Estimation of a common location parameter and of scale parameters

351

(4)

Estimation of P(X<Y) with data from sequential k-out-of-n systems

355

(7)

Reliability properties of sequential order statistics

362

(11)

Acknowledgement

367

(1)

References

367

(6)

PART V. PROGRESSIVE CENSORING

Progressive Censoring: A Review

373

(58)

Rita Aggarwal

Introduction

373

(1)

Review and notation

374

(2)

Moment determination

376

(19)

Inference under progressive censoring

395

(17)

Related topics in progressive censoring

412

(19)

References

426

(5)

Point and Interval Estimation for Parameters of the Logistic Distribution Based on Progressively Type-II Censored Samples

431

(26)

N. Balakrishnan

N. Kannan

Introduction

431

(2)

Maximum likelihood estimators

433

(1)

Approximate estimators

434

(3)

Weighted least squares estimation

437

(1)

Observed and expected Fisher information

438

(4)

Simulation results

442

(4)

Coverage probabilities

446

(8)

Illustrative Example

454

(1)

Conclusions

455

(2)

References

455

(2)

Progressively Censored Variables-Sampling Plans for Life Testing

457

(12)

Uditha Balasooriya

Introduction

459

(1)

Design of variables-sampling plans for progressively censored life-test experiments

459

(6)

Illustrations

465

(4)

References

466

(3)

PART VI. ANALYSIS FOR REPAIRABLE SYSTEMS

Graphical Techniques for Analysis of Data From Repairable Systems

469

(16)

Per Anders Akersten

Bengt Klefsjo

Bo Bergman

Introduction

469

(1)

Some concepts for repairable systems

470

(2)

The TTT-plot

472

(2)

Plotting inter-events times

474

(1)

Plotting event epochs

475

(1)

Combination of the two plots

476

(1)

Some useful test statistics

476

(2)

An example

478

(1)

A TTT-plot based on transformed data

479

(2)

Another example

481

(2)

Conclusion and comments

483

(2)

References

483

(2)

A Bayes Approach to the Problem of Making Repairs

485

(14)

Gary C. McDonald

Formulation of the problem

485

(1)

Bayes decision procedures

486

(1)

A univariate observation example

487

(4)

A bivariate observation example

491

(4)

Further comments on Bayes strategies

495

(4)

References

497

(2)

PART VII. ANALYSIS FOR MASKED DATA

Statistical Analysis for Masked Data

499

(24)

Betty J. Flehinger

Benjamin Reiser

Emmanual Yashchin

Introduction

500

(2)

Pass/fail case

502

(4)

Life time data: Independent competing risks

506

(13)

Life time data: Dependent competing risks

519

(4)

Acknowledgement

521

(1)

References

521

(2)

Analysis of Masked Failure Data under Competing Risks

523

(18)

Ananda Sen

Sanjib Basu

Mousumi Banerjee

Introduction

523

(1)

Parametric inference procedures

524

(10)

Non-parametric methodologies

534

(2)

Extensions and other directions

536

(5)

Acknowledgement

536

(2)

References

538

(3)

PART VIII. ANALYSIS FOR WARRANTY DATA

Warranty and Reliability

541

(44)

D. N. P. Murthy

W. R. Blischke

Introduction

541

(4)

Some common warranty policies

545

(6)

Warranty cost analysis

551

(17)

Engineering and management of reliability and warranty

568

(9)

Reliability and warranty data sources and analyses

577

(3)

Conclusions

580

(5)

References

581

(4)

Statistical Analysis of Reliability Warranty Data

585

(26)

Kazuyuki Suzuki

Rezaul Karim

Lianhua Wang

Introduction

585

(7)

Estimation of the number of warranty claims

592

(5)

Estimation of the failure time distribution using follow-up information

597

(4)

Estimation using the usage time distribution

601

(3)

Refinement

604

(2)

Conclusion

606

(5)

Acknowledgements

606

(1)

References

607

(4)

PART IX. ACCELERATED TESTING

Prediction of Field Reliability of Units, Each under Differing Dynamic Stresses, from Accelerated Test Data

611

(12)

Wayne Nelson

Introduction

611

(1)

Constant-stress model

612

(1)

A cumulative-exposure model for varying stresses

613

(2)

Model fitting

615

(2)

Estimate population reliability

617

(3)

Further work

620

(3)

Acknowledgements

621

(1)

References

621

(2)

Step-Stress Accelerated Life Test

623

(18)

E. Guono

N. Balakrishnan

Introduction

623

(1)

Step-Stress testing: Definitions

624

(1)

Acceleration models

625

(2)

Lifetime distribution under step-stress pattern

627

(3)

Inference

630

(3)

Non-Parametric approach

633

(1)

Bayesian analysis

634

(3)

Optimal test plan

637

(1)

Conclusion

638

(3)

References

638

(3)

PART X. DESTRUCTIVE TESTING

Estimation of Correlation under Destructive Testing

641

(18)

Richard Johnson

Wenquing Lu

Introduction

641

(1)

Current designs for estimating correlation

642

(4)

A new double proof load design

646

(6)

An example using the bivariate Weibull distribution

652

(1)

Nonparametric estimation of correlation and conditional survival

653

(6)

References

657

(2)

PART XI. TEST PLANS

System-Based Component Test Plans for Reliability Demonstration: A Review and Survey of the State-of-the-Art

659

(20)

Jayant Rajgopal

Mainak Mazumdar

Introduction

659

(5)

Review of research literature

664

(10)

Summary and future work

674

(5)

References

676

(3)

Life-Test Planning for Preliminary Screening of Materials: A Case Study

679

(14)

Jeff Stein

Necip Doganaksoy

Introduction

679

(1)

Case study background

680

(1)

Proposed approach to life-test planning

681

(5)

Life-test planning results for the proposed approach

686

(1)

Further considerations

686

(7)

Acknowledgments

691

(1)

Appendix A: Pseudo-code for simulation algorithm assuming a Weibull failure time distribution

691

(1)

Appendix B: Derivation of the scale parameter (α) for a fixed shape parameter (β) of a Weibull distribution

691

(1)

References

692

(1)

Analysis of Reliability Data from In-House Audit Laboratory Testing

693

(14)

Rekha Agrawal

Necip Doganaksoy

Introduction

693

(1)

The role of audit testing in reliability

694

(2)

Case study background

696

(2)

Using the mean cumulative function as a monitoring tool

698

(1)

Application to the case study

699

(3)

Observations, recommendations and conclusions

702

(5)

Acknowledgements

704

(1)

References

704

(3)

PART XII. SOFTWARE RELIABILITY

Software Reliability Modeling, Estimation and Analysis

707

(26)

M. Xie

G. Y. Hong

Introduction

707

(1)

Classification of software reliability models

707

(1)

Some important NHPP software reliability models

708

(13)

Markov software reliability models

721

(3)

Some Bayesian approaches

724

(3)

Some forecasting methods

727

(2)

Final remarks

729

(4)

References

730

(3)

Bayesian Analysis for Software Reliability Data

733

(16)

Jorge Alberto Achcar

Introduction

733

(3)

A Bayesian analysis for a special type-I strategy model: The Goel and Okumoto model

736

(1)

Bayesian inference for NHPP-I software reliability models

737

(2)

Bayesian inference for the superposition reliability models

739

(2)

A superposition model in the presence of a covariate

741

(3)

Bayesian inference and model determination

744

(1)

Some examples

745

(4)

References

747

(2)

PART XIII. INFERENTIAL METHODS

Direct Graphical Estimation for the Parameters in a Three-Parameter Weibull Distribution

749

(28)

Peter R. Nelson

K. B. Kulasekera

Introduction

750

(1)

Parameter estimation

751

(3)

Choice of r1, r2 and r3

754

(3)

A graphical solution

757

(5)

Comparison with other graphical procedures

762

(10)

Conclusion

772

(5)

Appendix

772

(3)

References

775

(2)

Bayesian and Frequentist Methods in Change-Point Problems

777

(12)

Nader Ebrahimi

Sujit K. Ghosh

Introduction

777

(1)

Continuous change-point problem

778

(4)

Discrete change-point problem

782

(3)

Concluding remarks

785

(4)

References

786

(3)

The Operating Characteristics of Sequential Procedures in Reliability

789

(24)

S. Zacks

Introduction

789

(1)

Sequential estimation of reliability with prescribed proportional closeness

790

(7)

Sequential testing

797

(5)

Reliability estimation after testing

802

(3)

The total operating time of repairable systems

805

(2)

Sequential detection of wearout

807

(1)

Sequential methods in software reliability

808

(5)

References

810

(3)

Simultaneous Selection of Extreme Populations from a Set of Two-Parameter Exponential Populations

813

(18)

Khaled Hussein

S. Panchapakesan

Introduction

813

(2)

Selection in terms of the location parameter: IZ approach

815

(4)

Selection in terms of the location parameter: SS approach

819

(3)

Selection in terms of the scale parameter: IZ approach

822

(2)

Selection in terms of the scale parameter: SS approach

824

(3)

Selection based on Type-II censored sample

827

(2)

Concluding remarks

829

(2)

References

829

(2)

Subject Index

831

(8)

Contents of Previous Volumes

839


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