Progressive Censoring

With its accessible style and concrete examples, the book is an essential resource and guide to the use of progressive censoring methodology in applied statistics and statistical reliability testing. Advanced students, practitioners and professionals will find it a useful guide to understanding and using progressive censoring concepts and methods in their work.

Auteur
N. BALAKRISHNAN, PhD, is Professor of Mathematics and Statistics at McMaster University in Hamilton, Ontario, Canada.V. B. NEVZOROV, PhD, DS, is Professor of Probability and Statistics at St. Petersburg State University in St. Petersburg, Russia.

Résumé
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.

Contenu
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.- 2.2 The Exponential Distribution: Spacings.- 2.3 The Uniform Distribution: Ratios.- 2.4 The Pareto Distribution: 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.- 4 Recursive Computation and Algorithms.- 4.1 Introduction.- 4.2 The Exponential Distribution.- 4.3 The Doubly Truncated Exponential Distribution.- 4.4 The Pareto Distribution and Truncated Forms.- 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.- 5.4 Other Relations for Moments.- 5.5 First-Order Approximations to the Moments.- 6 Linear Inference.- 6.1 One-Parameter (Scale) Models.- 6.2 Two-Parameter (Location-Scale) Models.- 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.- 8 Linear Prediction.- 8.1 Introduction.- 8.2 The Exponential Case.- 8.3 Case of General 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.- 9.4 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.- 10.4 The Extreme Value Distribution.- 10.5 The Extreme Value (II) Distribution.- 10.6 The Log-Normal Distribution.- 10.7 Tables.- 11 Acceptance Sampling Plans.- 11.1 Introduction.- 11.2 The Exponential Distribution.- 11.3 The Log-Normal Distribution.- Author Index.