Censored sampling arises in a life-testing experiment whenever the experimenter does not observe (either intentionally or unintentionally) the failure times of all units placed on a life-test. Inference based on censored sampling has been studied during the past 50 years by numerous authors for a wide range of lifetime distributions such as normal, exponential, gamma, Rayleigh, Weibull, extreme value, log-normal, inverse Gaussian, logistic, Laplace, and Pareto. Naturally, there are many different forms of censoring that have been discussed in the literature. In this book, we consider a versatile scheme of censoring called progressive Type-II censoring. Under this scheme of censoring, from a total of n units placed on a life-test, only m are completely observed until failure. At the time of the first failure, Rl of the n - 1 surviving units are randomly withdrawn (or censored) from the life-testing experiment. At the time of the next failure, R2 of the n - 2 -Rl surviving units are censored, and so on. Finally, at the time of the m-th failure, all the remaining Rm = n - m -Rl - . . . - Rm-l surviving units are censored. Note that censoring takes place here progressively in m stages. Clearly, this scheme includes as special cases the complete sample situation (when m = nand Rl = . . . = Rm = 0) and the conventional Type-II right censoring situation (when Rl = . . . = Rm-l = 0 and Rm = n - m).
Inhaltsverzeichnis
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.
