Reliability analysis of constant partially accelerated life tests under progressive first failure type-II censored data from Lomax model: EM and MCMC algorithms

Mohamed S. Eliwa; Essam A. Ahmed; Mohamed S. Eliwa; Essam A. Ahmed

doi:10.3934/math.2023002

AIMS Mathematics

2023, Volume 8, Issue 1: 29-60. doi: 10.3934/math.2023002

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Research article

Reliability analysis of constant partially accelerated life tests under progressive first failure type-II censored data from Lomax model: EM and MCMC algorithms

Mohamed S. Eliwa ^{1,2,3
,
, ,},
Essam A. Ahmed ^4,5

1.
Department of Statistics and Operation Research, College of Science, Qassim University, Buraydah 51482, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
3.
Department of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy
4.
Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt
5.
Faculty of Business Administration, Taibah University, Saudi Arabia

Received: 19 July 2022 Revised: 25 August 2022 Accepted: 01 September 2022 Published: 27 September 2022
MSC : 60E05, 62F10, 62N05, 62P10

Examining life-testing experiments on a product or material usually requires a long time of monitoring. To reduce the testing period, units can be tested under more severe than normal conditions, which are called accelerated life tests (ALTs). The objective of this study is to investigate the problem of point and interval estimations of the Lomax distribution under constant stress partially ALTs based on progressive first failure type-II censored samples. The point estimates of unknown parameters and the acceleration factor are obtained by using maximum likelihood and Bayesian approaches. Since reliability data are censored, the maximum likelihood estimates (MLEs) are derived utilizing the general expectation-maximization (EM) algorithm. In the process of Bayesian inference, the Bayes point estimates as well as the highest posterior density credible intervals of the model parameters and acceleration factor, are reported. This is done by using the Markov Chain Monte Carlo (MCMC) technique concerning both symmetric (squared error) and asymmetric (linear-exponential and general entropy) loss functions. Monte Carlo simulation studies are performed under different sizes of samples for comparison purposes. Finally, the proposed methods are applied to oil breakdown times of insulating fluid under two high-test voltage stress level data.
- constant-stress partially ALTs,
- Bayesian estimation,
- expectation-maximization algorithm,
- metropolis-Hasting algorithm
Citation: Mohamed S. Eliwa, Essam A. Ahmed. Reliability analysis of constant partially accelerated life tests under progressive first failure type-II censored data from Lomax model: EM and MCMC algorithms[J]. AIMS Mathematics, 2023, 8(1): 29-60. doi: 10.3934/math.2023002

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Abstract

Examining life-testing experiments on a product or material usually requires a long time of monitoring. To reduce the testing period, units can be tested under more severe than normal conditions, which are called accelerated life tests (ALTs). The objective of this study is to investigate the problem of point and interval estimations of the Lomax distribution under constant stress partially ALTs based on progressive first failure type-II censored samples. The point estimates of unknown parameters and the acceleration factor are obtained by using maximum likelihood and Bayesian approaches. Since reliability data are censored, the maximum likelihood estimates (MLEs) are derived utilizing the general expectation-maximization (EM) algorithm. In the process of Bayesian inference, the Bayes point estimates as well as the highest posterior density credible intervals of the model parameters and acceleration factor, are reported. This is done by using the Markov Chain Monte Carlo (MCMC) technique concerning both symmetric (squared error) and asymmetric (linear-exponential and general entropy) loss functions. Monte Carlo simulation studies are performed under different sizes of samples for comparison purposes. Finally, the proposed methods are applied to oil breakdown times of insulating fluid under two high-test voltage stress level data.

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