Progressive censoring : theory, methods, and applications
著者
書誌事項
Progressive censoring : theory, methods, and applications
（Statistics for industry and technology）
Birkhäuser, c2000
- : us
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注記
Includes bibliographical references (p. 223-234) and indexes
内容説明・目次
- 巻冊次
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: us ISBN 9780817640019
内容説明
This new book offers a guide to the theory and methods of progressive censoring. In many industrial experiments involving lifetimes of machines or units, experiments have to be terminated early. Progressive Censoring first introduces progressive sampling foundations, and then discusses various properties of progressive samples. The book points out the greater efficiency gained by using this scheme instead of classical right-censoring methods.
目次
1 Introduction.- 1.1 The Big Picture.- 1.2 Genesis.- 1.3 The Need for Progressive Censoring.- 1.4 A Relatively Unexplored Idea.- 1.5 Mathematical Notations.- 1.6 A Friendly Note.- 2 Mathematical Properties of Progressively Type-II Right Censored Order Statistics.- 2.1 General Continuous Distributions.- 2.1.1 Introduction.- 2.1.2 Results.- 2.2 The Exponential Distribution: Spacings.- 2.2.1 Introduction.- 2.2.2 Progressively Type-II Right Censored Spacings.- 2.2.3 Deriving Moments Using Independent Spacings.- 2.3 The Uniform Distribution: Ratios.- 2.3.1 Introduction.- 2.3.2 Independent Ratios.- 2.3.3 Deriving Moments Using Independent Ratios.- 2.4 The Pareto Distribution: Ratios.- 2.4.1 Introduction.- 2.4.2 Independent Ratios.- 2.4.3 Deriving Moments Using Independent Ratios.- 2.5 Bounds for Means and Variances.- 3 Simulational Algorithms.- 3.1 Introduction.- 3.2 Simulation Using the Uniform Distribution.- 3.3 Simulation Using the Exponential Distribution.- 3.4 General Progressively Type-II Censored Samples.- 3.4.1 Arbitrary Continuous Distributions.- 3.4.2 The Exponential Distribution.- 3.4.3 The Uniform Distribution.- 4 Recursive Computation and Algorithms.- 4.1 Introduction.- 4.2 The Exponential Distribution.- 4.2.1 Recurrence Relations for Single Moments.- 4.2.2 Recurrence Relations for Product Moments.- 4.2.3 Recursive Algorithm.- 4.3 The Doubly Truncated Exponential Distribution.- 4.3.1 Recurrence Relations for Single Moments.- 4.3.2 Recurrence Relations for Product Moments.- 4.3.3 Recursive Algorithm.- 4.4 The Pareto Distribution and Truncated Forms.- 4.4.1 Recurrence Relations for Single Moments.- 4.4.2 Recurrence Relations for Product Moments.- 4.4.3 Recursive Algorithm.- 4.5 The Power Function Distribution and Truncated Forms.- 5 Alternative Computational Methods.- 5.1 Introduction.- 5.2 Formulas in Terms of Moments of Usual Order Statistics.- 5.3 Formulas in the Case of Symmetric Distributions.- 5.3.1 Progressive Withdrawal.- 5.3.2 Properties of Progressively Type-II Left Withdrawn Order Statistics.- 5.3.3 Moments of Progressively Type-II Right Censored Order Statistics from Symmetric Distributions.- 5.4 Other Relations for Moments.- 5.5 First-Order Approximations to the Moments.- 6 Linear Inference.- 6.1 One-Parameter (Scale) Models.- 6.1.1 Introduction.- 6.1.2 The Exponential Distribution.- 6.1.3 The Uniform Distribution.- 6.1.4 The Pareto Distribution.- 6.1.5 First-Order Approximation to the BLUE.- 6.2 Two-Parameter (Location-Scale) Models.- 6.2.1 Introduction.- 6.2.2 The Exponential Distribution.- 6.2.3 The Uniform Distribution.- 6.2.4 The Pareto Distribution.- 6.2.5 The Laplace Distribution.- 6.2.6 The Extreme Value Distribution.- 6.2.7 First-Order Approximations to the BLUEs.- 6.3 Best Linear Invariant Estimation.- 7 Likelihood Inference: Type-I and Type-II Censoring.- 71. Introduction.- 7.2 General Continuous Distributions.- 7.3 Specific Continuous Distributions.- 7.3.1 The Normal Distribution.- 7.3.2 The Exponential Distribution.- 7.3.3 The Weibull Distribution.- 7.3.4 The Uniform Distribution.- 7.3.4 The Pareto Distribution.- 7.3.6 The Laplace Distribution.- 7.3.7 Other Distributions (Log-Normal, Gamma, Burr).- 8 Linear Prediction.- 8.1 Introduction.- 8.2 The Exponential Case.- 8.3 Case of General Distributions.- 8.3.1 Scale-Parameter Distributions.- 8.3.2 Location-Scale Distributions.- 8.4 A Simple Approach Based on BLUEs.- 8.5 First-Order Approximations to BLUPs.- 8.6 Prediction Intervals.- 8.7 Illustrative Examples.- 9 Conditional Inference.- 9.1 Introduction.- 9.2 Inference for Location and Scale Parameters.- 9.3 Inference for Quantiles and Reliability and Prediction Intervals.- 9.3.1 Inference for Quantiles.- 9.3.2 Inference for Reliability.- 9.3.3 Prediction Intervals for Future Failures.- 9.4 Results for Extreme Value Distribution.- 9.5 Results for Exponential Distribution.- 9.6 Illustrative Examples.- 9.7 Results for Pareto Distribution.- 10 Optimal Censoring Schemes.- 10.1 Introduction.- 10.2 The Exponential Distribution.- 10.3 The Normal Distribution.- 10.3.1 Discussion of Results.- 10.4 The Extreme Value Distribution.- 10.4.1 Discussion of Results.- 10.5 The Extreme Value (II) Distribution.- 10.5.1 Discussion of Results.- 10.6 The Log-Normal Distribution.- 10.6.1 Discussion of Results.- 10.7 Tables.- 11 Acceptance Sampling Plans.- 11.1 Introduction.- 11.2 The Exponential Distribution.- 11.2.1 One-Sided Sampling Plans.- 11.2.2 Two-Sided Sampling Plans.- 11.3 The Log-Normal Distribution.- Author Index.
- 巻冊次
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ISBN 9783764340018
内容説明
This new volume offers a throughout guide to the theory and methods of progressive censoring for practitioners and professionals in applied statistics, quality control, life testing and reliability testing. In many industrial experiments involving lifetimes of machines or units, experiments have to be terminated early due to a variety of circumstances. Samples that arise from such experiments are called censored samples, and a new efficient alternative method is referred to as "progressive censoring" (where the removal of live units at time of failure is employed). This book first introduces progressive sampling foundations, then discusses various properties of progressive samples. It also describes how to make exact or approximate inferences for the difference statistical models with samples based on progressive censoring schemes. With many concrete examples, the book points out the greater efficiency gained by suing this scheme instead of classical right-censorship methods. With its accessible style and examples, the book should be an essential resource for progressive censoring methodology.
Advanced students, practitioners, and professionals in applied statistics, reliability and life-testing research should find it a useful guide to understanding and using this new methodology in their work.
目次
- Introduction
- mathematics properties of progressively type-II right censored order statistics
- simulational algorithms
- recursive computation and algorithms
- alternative computational methods
- linear inference
- likelihood inference - type-I and type-II censoring
- linear prediction
- conditional inference
- optimal censoring schemes
- acceptance sampling plans.
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