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Progressive Censoring Theory, Methods, and Applications

Balakrishnan N. Aggarwala Rita
Heftet / 2012 / Engelsk

Produktdetaljer

ISBN
9781461270997
Publisert
2012-10-16
Utgiver
Vendor
Springer-Verlag New York Inc.
Høyde
254 mm
Bredde
178 mm
Aldersnivå
Research, P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet

Forfatter
Balakrishnan N.
Aggarwala Rita

Progressive Censoring Theory, Methods, and Applications

Balakrishnan N. Aggarwala Rita
Heftet / 2012 / Engelsk
Balakrishnan N. Aggarwala Rita
Heftet / 2012 / Engelsk
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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 At the time of the first failure, Rl of the n - 1 surviving units are randomly withdrawn (or censored) from the life-testing experiment.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).
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Finally, at the time of the m-th failure, all the remaining Rm = n - m -Rl - . = Rm = 0) and the conventional Type-II right censoring situation (when Rl = . = Rm-l = 0 and Rm = n - m).
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.
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GPSR Compliance The European Union's (EU) General Product Safety Regulation (GPSR) is a set of rules that requires consumer products to be safe and our obligations to ensure this. If you have any concerns about our products you can contact us on ProductSafety@springernature.com. In case Publisher is established outside the EU, the EU authorized representative is: Springer Nature Customer Service Center GmbH Europaplatz 3 69115 Heidelberg, Germany ProductSafety@springernature.com
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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).
Les mer
Finally, at the time of the m-th failure, all the remaining Rm = n - m -Rl - . = Rm = 0) and the conventional Type-II right censoring situation (when Rl = . = Rm-l = 0 and Rm = n - m).
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.
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Springer Book Archives
Springer Book Archives
GPSR Compliance The European Union's (EU) General Product Safety Regulation (GPSR) is a set of rules that requires consumer products to be safe and our obligations to ensure this. If you have any concerns about our products you can contact us on ProductSafety@springernature.com. In case Publisher is established outside the EU, the EU authorized representative is: Springer Nature Customer Service Center GmbH Europaplatz 3 69115 Heidelberg, Germany ProductSafety@springernature.com
Les mer

Produktdetaljer

ISBN
9781461270997
Publisert
2012-10-16
Utgiver
Vendor
Springer-Verlag New York Inc.
Høyde
254 mm
Bredde
178 mm
Aldersnivå
Research, P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet

Forfatter
Balakrishnan N.
Aggarwala Rita

Relaterte produkter