Statistical Analysis and Theoretical Framework for a Partially Accelerated Life Test Model with Progressive First Failure Censoring Utilizing a Power Hazard Distribution

Amel Abd-El-Monem, Mohamed S. Eliwa (), Mahmoud El-Morshedy, Afrah Al-Bossly and Rashad M. EL-Sagheer
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Amel Abd-El-Monem: Department of Mathematics, Faculty of Education, Ain-Shams University, Cairo 11566, Egypt
Mohamed S. Eliwa: Department of Statistics and Operation Research, College of Science, Qassim University, Buraydah 51482, Saudi Arabia
Mahmoud El-Morshedy: Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
Afrah Al-Bossly: Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
Rashad M. EL-Sagheer: Mathematics Department, Faculty of Science, Al-Azhar University, Naser City, Cairo 11884, Egypt

Mathematics, 2023, vol. 11, issue 20, 1-21

Abstract: Monitoring life-testing trials for a product or substance often demands significant time and effort. To expedite this process, sometimes units are subjected to more severe conditions in what is known as accelerated life tests. This paper is dedicated to addressing the challenge of estimating the power hazard distribution, both in terms of point and interval estimations, during constant- stress partially accelerated life tests using progressive first failure censored samples. Three techniques are employed for this purpose: maximum likelihood, two parametric bootstraps, and Bayesian methods. These techniques yield point estimates for unknown parameters and the acceleration factor. Additionally, we construct approximate confidence intervals and highest posterior density credible intervals for both the parameters and acceleration factor. The former relies on the asymptotic distribution of maximum likelihood estimators, while the latter employs the Markov chain Monte Carlo technique and focuses on the squared error loss function. To assess the effectiveness of these estimation methods and compare the performance of their respective confidence intervals, a simulation study is conducted. Finally, we validate these inference techniques using real-life engineering data.

Keywords: statistical model; power hazard distribution; constant stress partially accelerated life tests; Bayes theorem; progressive first failure censored; parametric bootstrap; computer simulation; statistics and numerical data (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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