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Estimation in Step-Stress Accelerated Life Tests for Power Generalized Weibull Distribution with Progressive Censoring


Affiliations
1 Department of Mathematics, Al-Azhar University, Cairo, Egypt
2 Department of Mathematics, Ain Shams University, Cairo, Egypt
 

Based on progressive censoring, step-stress partially accelerated life tests are considered when the lifetime of a product follows power generalized Weibull distribution. The maximum likelihood estimates (MLEs) and Bayes estimates (BEs) are obtained for the distribution parameters and the acceleration factor. In addition, the approximate and bootstrap confidence intervals (CIs) of the estimators are presented. Furthermore, the optimal stress change time for the step-stress partially accelerated life test is determined by minimizing the asymptotic variance of MLEs of themodel parameters and the acceleration factor. Simulation results are carried out to study the precision of the MLEs and BEs for the parameters involved.
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  • Estimation in Step-Stress Accelerated Life Tests for Power Generalized Weibull Distribution with Progressive Censoring

Abstract Views: 101  |  PDF Views: 7

Authors

M. M. Mohie EL-Din
Department of Mathematics, Al-Azhar University, Cairo, Egypt
S. E. Abu-Youssef
Department of Mathematics, Al-Azhar University, Cairo, Egypt
Nahed S. A. Ali
Department of Mathematics, Ain Shams University, Cairo, Egypt
A. M. Abd El-Raheem
Department of Mathematics, Ain Shams University, Cairo, Egypt

Abstract


Based on progressive censoring, step-stress partially accelerated life tests are considered when the lifetime of a product follows power generalized Weibull distribution. The maximum likelihood estimates (MLEs) and Bayes estimates (BEs) are obtained for the distribution parameters and the acceleration factor. In addition, the approximate and bootstrap confidence intervals (CIs) of the estimators are presented. Furthermore, the optimal stress change time for the step-stress partially accelerated life test is determined by minimizing the asymptotic variance of MLEs of themodel parameters and the acceleration factor. Simulation results are carried out to study the precision of the MLEs and BEs for the parameters involved.