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2014 | Buch

Progressive Censoring: Data and Models Kapitel lesen Erstes Kapitel lesen

The Art of Progressive Censoring

Applications to Reliability and Quality

verfasst von: N. Balakrishnan, Erhard Cramer

Verlag: Springer New York

Buchreihe : Statistics for Industry and Technology

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This monograph offers a thorough and updated guide to the theory and methods of progressive censoring, an area that has experienced tremendous growth in recent years. Progressive censoring, originally proposed in the 1950s, is an efficient method of handling samples from industrial experiments involving lifetimes of units that have either failed or censored in a progressive fashion during the life test, with many practical applications to reliability and quality.

Key topics and features:

Data sets from the literature as well as newly simulated data sets are used to illustrate concepts throughout the textEmphasis on real-life applications to life testing, reliability, and quality controlDiscussion of parametric and nonparametric inferenceCoverage of experimental design with optimal progressive censoring

The Art of Progressive Censoring is a valuable reference for graduate students, researchers, and practitioners in applied statistics, quality control, life testing, and reliability. With its accessible style and concrete examples, the work may also be used as a textbook in advanced undergraduate or beginning graduate courses on censoring or progressive censoring, as well as a supplementary textbook for a course on ordered data.

Inhaltsverzeichnis

Frontmatter

Distribution Theory and Models

Frontmatter
Chapter 1. Progressive Censoring: Data and Models
Abstract
The notion of progressive censoring is explained by introducing progressive Type-I and Type-II censoring in detail. The presentation includes detailed descriptions of the procedures as well as graphical illustrations and data. Additionally, progressive hybrid censoring is discussed. Finally, the chapter is supplemented by introducing particular probability models assumed in progressive censoring.
N. Balakrishnan, Erhard Cramer
Chapter 2. Progressive Type-II Censoring: Distribution Theory
Abstract
The distribution theory of progressively Type-II censored order statistics is presented with a focus on particular baseline distributions like exponential and generalized Pareto distributions. The discussion includes joint, marginal, and conditional distributions as well as the fundamental quantile representation. The connection to generalized order statistics and sequential order statistics is highlighted. Further topics discussed are shapes of density functions, recurrence relations, exceedances, and discrete progressively Type-II censored order statistics.
N. Balakrishnan, Erhard Cramer
Chapter 3. Further Distributional Results on Progressive Type-II Censoring
Abstract
Further probabilistic results on progressively Type-II censored order statistics are summarized. First, characterization and stochastic ordering results are reviewed. After discussing aging properties, limiting and extreme value results are discussed. Finally, the notion of near minimum progressively Type-II censored order statistics is addressed.
N. Balakrishnan, Erhard Cramer
Chapter 4. Progressive Type-I Censoring: Basic Properties
Abstract
The distribution theory of progressive Type-I censored order statistics is presented. Furthermore, the dependence structure and the distribution of the number of observations up to some given threshold are addressed.
N. Balakrishnan, Erhard Cramer
Chapter 5. Progressive Hybrid Censoring: Distributions and Properties
Abstract
The distribution theory of progressive hybrid censored order statistics is developed. A special emphasis is given to the exponential distribution where also the distributions of spacings and the total time on test statistic are discussed.
N. Balakrishnan, Erhard Cramer
Chapter 6. Adaptive Progressive Type-II Censoring and Related Models
Abstract
The notion of adaptive progressive Type-II censoring is introduced in detail and the relation to some other models is illustrated. The discussion includes, e.g., nonadapative progressive Type-II censoring, the Ng–Kundu–Chan model, and progressive censoring with random removals.
N. Balakrishnan, Erhard Cramer
Chapter 7. Moments of Progressively Type-II Censored Order Statistics
Abstract
Results on moments of progressively Type-II censored order statistics are reviewed. After presenting general expressions and existence results, explicit expressions for particular population distributions are given. Further, results for symmetric population distributions are developed. The presentation is completed by a survey on reccurence relations, bounds, and first-order approximations.
N. Balakrishnan, Erhard Cramer
Chapter 8. Simulation of Progressively Censored Order Statistics
Abstract
Several accounts to the simulation of progressively censored data are presented. This includes procedures mimicking the generation process ofprogressively censored order statistics as well as methods based on the quantile representation.
N. Balakrishnan, Erhard Cramer
Chapter 9. Information Measures
Abstract
Several information measures and corresponding expressions are presented for progressively censored samples. The discussion includes Fisher information, entropy, Kullback–Leibler information, Pitman closeness, and Tukey's linear sensitivity measure.
N. Balakrishnan, Erhard Cramer
Chapter 10. Progressive Type-II Censoring Under Nonstandard Conditions
Abstract
The mixture representation for progressively Type-II censored order statistics from arbitrary baseline distributions is proven. Furthermore, results for INID progressively Type-II censored order statistics and their connection to permanents are shown. Finally, results on progressively censored samples from dependent samples are presented.
N. Balakrishnan, Erhard Cramer

Inference

Frontmatter
Chapter 11. Linear Estimation in Progressive Type-II Censoring
Abstract
Linear inference for progressively Type-II censored order statistics is discussed for location, scale, and location-scale families of population distributions. After a general introduction, results for exponential, generalized Pareto, extreme value, Weibull, Laplace, and logistic distributions are presented in detail.
N. Balakrishnan, Erhard Cramer
Chapter 12. Maximum Likelihood Estimation in Progressive Type-II Censoring
Abstract
Likelihood inference in progressive Type-II censoring is presented for a wide range of distributions including exponential, Weibull, extreme value, generalized Pareto, Laplace, and normal distributions. The chapter is supplemented by a review for other distributions as well as by a discussion of related methods like modified and approximate likelihood estimation. Finally, results for $M$-estimation and order restricted inference are presented.
N. Balakrishnan, Erhard Cramer
Chapter 13. Point Estimation in Progressive Type-I Censoring
Abstract
Results on likelihood inference in progressive Type-I censoring are reviewed for a plenty of distributions including one- and two-parameter exponential, extreme value, Weibull, normal, and Burr distributions.
N. Balakrishnan, Erhard Cramer
Chapter 14. Progressive Hybrid and Adaptive Censoring and Related Inference
Abstract
Inferential results for progressive hybrid and adaptive progressive Type-II censored data are shown. A special focus is given to one- and two-parameter exponential distributions.
N. Balakrishnan, Erhard Cramer
Chapter 15. Bayesian Inference for Progressively Type-II Censored Data
Abstract
Bayesian approaches for progressively Type-II censored data are reviewed. The presentation includes, e.g., exponential, Weibull, Pareto, and Burr distributions.
N. Balakrishnan, Erhard Cramer
Chapter 16. Point Prediction from Progressively Type-II Censored Samples
Abstract
Several prediction problems for progressively Type-II censored data are considered. This includes prediction of progressively censored lifetime as well as prediction of future observations. After introducing several concepts of point prediction, applications to exponential, extreme value, normal, and Pareto distributions are presented.
N. Balakrishnan, Erhard Cramer
Chapter 17. Statistical Intervals for Progressively Type-II Censored Data
Abstract
Results on interval prediction based on progressively Type-II censored order statistics are reviewed. The discussion includes exact, conditional, and asymptotic confidence intervals as well as prediction and tolerance intervals.
N. Balakrishnan, Erhard Cramer
Chapter 18. Progressive Type-I Interval Censored Data
Abstract
Inference for progressive Type-I interval censored data is presented. The discussion includes parametric inference as well as problems of choosing optimal inspection times and optimal progressive interval censoring proportions.
N. Balakrishnan, Erhard Cramer
Chapter 19. Goodness-of-Fit Tests in Progressive Type-II Censoring
Abstract
Goodness-of-fit tests for progressively Type-II censored data are reviewed. The presentation includes tests on exponentiality as well as tests for other distributional assumptions.
N. Balakrishnan, Erhard Cramer
Chapter 20. Counting and Quantile Processes and Progressive Censoring
Abstract
Results for counting and quantile processes based on progressively Type-II censored data are presented.
N. Balakrishnan, Erhard Cramer
Chapter 21. Nonparametric Inferential Issues in Progressive Type-II Censoring
Abstract
Nonparametric statistical tests are reviewed. This includes precedence-type tests as well as test for hazard rate ordering.
N. Balakrishnan, Erhard Cramer

Applications in Survival Analysis and Reliability

Frontmatter
Chapter 22. Acceptance Sampling Plans
Abstract
Results for reliability/acceptance sampling plans based on progressively Type-II censored data are reviewed. This includes results for exponential, Weibull, and log-normal lifetimes. Furthermore, capability indices are discussed.
N. Balakrishnan, Erhard Cramer
Chapter 23. Accelerated Life Testing
Abstract
Methods of accelerated life testing are applied to several kinds of progressively censored data. This includes step-stress testing as well as progressive stress models.
N. Balakrishnan, Erhard Cramer
Chapter 24. Stress–Strength Models with Progressively Censored Data
Abstract
Step-stress models based on two progressively Type-II censored data sets are reviewed. The discussion includes likelihood inference as well minimum variance unbiased estimation. A special emphasis is put on exponentially distributed stress and strength.
N. Balakrishnan, Erhard Cramer
Chapter 25. Multi-sample Models
Abstract
Several models involving multiple samples based on progressively Type-II censored data are discussed. The presentation includes competing risk models, joint progressive censoring, concomitants, and progressively censored systems data.
N. Balakrishnan, Erhard Cramer
Chapter 26. Optimal Experimental Designs
Abstract
The problem of an optimal censoring plan in progressive Type-II censoring is discussed for several criteria including minimum experimental time, maximum Fisher information, minimum variance of estimates, as well as further criteria proposed in the literature.
N. Balakrishnan, Erhard Cramer
Backmatter
Metadaten
Titel
The Art of Progressive Censoring
verfasst von
N. Balakrishnan
Erhard Cramer
Copyright-Jahr
2014
Verlag
Springer New York
Electronic ISBN
978-0-8176-4807-7
Print ISBN
978-0-8176-4806-0
DOI
https://doi.org/10.1007/978-0-8176-4807-7

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