Reliability analysis at usual operating settings for Weibull Constant-stress model with improved adaptive Type-Ⅱ progressively censored samples

Mazen Nassar; Refah Alotaibi; Ahmed Elshahhat; Mazen Nassar; Refah Alotaibi; Ahmed Elshahhat

doi:10.3934/math.2024823

AIMS Mathematics

2024, Volume 9, Issue 7: 16931-16965. doi: 10.3934/math.2024823

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Reliability analysis at usual operating settings for Weibull Constant-stress model with improved adaptive Type-Ⅱ progressively censored samples

1.
Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
2.
Department of Statistics, Faculty of Commerce, Zagazig University, Zagazig 44519, Egypt
3.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
4.
Faculty of Technology and Development, Zagazig University, Zagazig 44519, Egypt

Received: 27 February 2024 Revised: 09 April 2024 Accepted: 06 May 2024 Published: 15 May 2024
MSC : 62F10, 62F15, 62N01, 62N02, 62N05

An improved adaptive Type-Ⅱ progressive censoring scheme was recently introduced to ensure that the examination duration will not surpass a specified threshold span. Employing this plan, this paper aimed to investigate statistical inference using Weibull constant-stress accelerated life tests. Two classical setups, namely maximum likelihood and maximum product of spacings, were explored to estimate the scale, shape, and reliability index under normal use conditions as well as their asymptotic confidence intervals. Through the same suggested classical setups, the Bayesian estimation methodology via the Markov chain Monte Carlo technique based on the squared error loss was considered to acquire the point and credible estimates. To compare the efficiency of the various offered approaches, a simulation study was carried out with varied sample sizes and censoring designs. The simulation findings show that the Bayesian approach via the likelihood function provides better estimates when compared with other methods. Finally, the utility of the proposed techniques was illustrated by analyzing two real data sets indicating the failure times of a white organic light-emitting diode and a pump motor.
Citation: Mazen Nassar, Refah Alotaibi, Ahmed Elshahhat. Reliability analysis at usual operating settings for Weibull Constant-stress model with improved adaptive Type-Ⅱ progressively censored samples[J]. AIMS Mathematics, 2024, 9(7): 16931-16965. doi: 10.3934/math.2024823

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Abstract

An improved adaptive Type-Ⅱ progressive censoring scheme was recently introduced to ensure that the examination duration will not surpass a specified threshold span. Employing this plan, this paper aimed to investigate statistical inference using Weibull constant-stress accelerated life tests. Two classical setups, namely maximum likelihood and maximum product of spacings, were explored to estimate the scale, shape, and reliability index under normal use conditions as well as their asymptotic confidence intervals. Through the same suggested classical setups, the Bayesian estimation methodology via the Markov chain Monte Carlo technique based on the squared error loss was considered to acquire the point and credible estimates. To compare the efficiency of the various offered approaches, a simulation study was carried out with varied sample sizes and censoring designs. The simulation findings show that the Bayesian approach via the likelihood function provides better estimates when compared with other methods. Finally, the utility of the proposed techniques was illustrated by analyzing two real data sets indicating the failure times of a white organic light-emitting diode and a pump motor.

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