Open Access

ARTICLE

Bayesian Analysis in Partially Accelerated Life Tests for Weighted Lomax Distribution

Rashad Bantan¹, Amal S. Hassan², Ehab Almetwally³, M. Elgarhy⁴, Farrukh Jamal⁵, Christophe Chesneau⁶, Mahmoud Elsehetry^7,*

1 Deanship of Scientific Research, King Abdulaziz University, Jeddah, 21589, Kingdom of Saudi Arabia
2 Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, 12613, Egypt
3 Faculty of Business Administration, Delta University of Science and Technology, Mansoura, 11152, Egypt
4 The Higher Institute of Commercial Sciences, Al Mahalla Al Kubra, 31951, Algarbia, Egypt
5 Department of Statistics, The Islamia University of Bahawalpur, Punjab 63100, Pakistan
6 Department of Mathematics, LMNO, University of Caen, Caen, 14032, France
7 Deanship of Information Technology, King Abdulaziz University, Jeddah, 21589, Kingdom of Saudi Arabia

* Corresponding Author: Mahmoud Elsehetry. Email:

Computers, Materials & Continua 2021, 68(3), 2859-2875. https://doi.org/10.32604/cmc.2021.015422

Received 20 November 2020; Accepted 23 February 2021; Issue published 06 May 2021

Abstract

Accelerated life testing has been widely used in product life testing experiments because it can quickly provide information on the lifetime distributions by testing products or materials at higher than basic conditional levels of stress, such as pressure, temperature, vibration, voltage, or load to induce early failures. In this paper, a step stress partially accelerated life test (SS-PALT) is regarded under the progressive type-II censored data with random removals. The removals from the test are considered to have the binomial distribution. The life times of the testing items are assumed to follow length-biased weighted Lomax distribution. The maximum likelihood method is used for estimating the model parameters of length-biased weighted Lomax. The asymptotic confidence interval estimates of the model parameters are evaluated using the Fisher information matrix. The Bayesian estimators cannot be obtained in the explicit form, so the Markov chain Monte Carlo method is employed to address this problem, which ensures both obtaining the Bayesian estimates as well as constructing the credible interval of the involved parameters. The precision of the Bayesian estimates and the maximum likelihood estimates are compared by simulations. In addition, to compare the performance of the considered confidence intervals for different parameter values and sample sizes. The Bootstrap confidence intervals give more accurate results than the approximate confidence intervals since the lengths of the former are less than the lengths of latter, for different sample sizes, observed failures, and censoring schemes, in most cases. Also, the percentile Bootstrap confidence intervals give more accurate results than Bootstrap-t since the lengths of the former are less than the lengths of latter for different sample sizes, observed failures, and censoring schemes, in most cases. Further performance comparison is conducted by the experiments with real data.

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