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2002•Communication in Statistics- Theory and MethodsRequires access

THE MAXIMUM LIKELIHOOD ESTIMATES IN STEP PARTIALLY ACCELERATED LIFE TESTS FOR THE WEIBULL PARAMETERS IN CENSORED DATA

Abdalla Abdel-Ghaly, Ahmed F. Attia, Magda M. Abdel-Ghani

Open publisher page 31 citations

Abstract

This paper considers the estimation problem in step partially accelerated life tests in which test items are first run simultaneously at use condition for a specified time, and the surviving items are then run at accelerated condition until a predetermined censoring time. The lifetime of these items is assumed to follow the Weibull distribution. The maximum likelihood estimates (MLEs) are obtained for the distribution parameters and the acceleration factor in both type-I and type-II censored samples. The modified quasilinearization method is used to solve the nonlinear maximum likelihood equations. Also, the confidence intervals of the estimators are obtained. Simulation results are given for different sized samples studying the precision and variation of MLEs such as the relative absolute bias, mean square error and the relative error.

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What this paper is about

This paper considers the estimation problem in step partially accelerated life tests in which test items are first run simultaneously at use condition for a specified time, and the surviving items are then run at accelerated condition until a predetermined censoring time. The lifetime of these items is assumed to follow the Weibull distribution. The maximum likelihood estimates (MLEs) are obtained for the distribution parameters and the acceleration factor in both type-I and type-II censored samples. The modified quasilinearization method is used to solve the nonlinear maximum likelihood equations. Also, the confidence intervals of the estimators are obtained. Simulation results are given for different sized samples studying the precision and variation of MLEs such as the relative absolute bias, mean square error and the relative error.

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Available abstract

This paper considers the estimation problem in step partially accelerated life tests in which test items are first run simultaneously at use condition for a specified time, and the surviving items are then run at accelerated condition until a predetermined censoring time. The lifetime of these items is assumed to follow the Weibull distribution. The maximum likelihood estimates (MLEs) are obtained for the distribution parameters and the acceleration factor in both type-I and type-II censored samples. The modified quasilinearization method is used to solve the nonlinear maximum likelihood equations. Also, the confidence intervals of the estimators are obtained. Simulation results are given for different sized samples studying the precision and variation of MLEs such as the relative absolute bias, mean square error and the relative error.

Key concepts: Weibull distribution, Censoring (clinical trials), Statistics, Mathematics, Estimator, Maximum likelihood, Exponentiated Weibull distribution

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