Analysis of Weibull progressively first-failure censored data with beta-binomial removals

Refah Alotaibi; Mazen Nassar; Zareen A. Khan; Ahmed Elshahhat; Refah Alotaibi; Mazen Nassar; Zareen A. Khan; Ahmed Elshahhat

doi:10.3934/math.20241172

AIMS Mathematics

2024, Volume 9, Issue 9: 24109-24142. doi: 10.3934/math.20241172

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Analysis of Weibull progressively first-failure censored data with beta-binomial removals

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

Received: 06 June 2024 Revised: 28 July 2024 Accepted: 31 July 2024 Published: 14 August 2024
MSC : 62F10, 62F15, 62N01, 62N02, 62N05

This study examined the estimations of Weibull distribution using progressively first-failure censored data, under the assumption that removals follow the beta-binomial distribution. Classical and Bayesian approaches for estimating unknown model parameters have been established. The estimations included scale and shape parameters, reliability and failure rate metrics as well as beta-binomial parameters. Estimations were considered from both point and interval viewpoints. The Bayes estimates were developed by using the squared error loss and generating samples for the posterior distribution through the Markov Chain Monte Carlo technique. Two interval estimation approaches are considered: approximate confidence intervals based on asymptotic normality of likelihood estimates and Bayes credible intervals. To investigate the performance of classical and Bayesian estimations, a simulation study was considered by various kinds of experimental settings. Furthermore, two examples related to real datasets were thoroughly investigated to verify the practical importance of the suggested methodologies.
- Weibull distribution,
- progressive first-failure censoring,
- beta-binomial removals,
- classical estimation,
- Bayesian estimation
Citation: Refah Alotaibi, Mazen Nassar, Zareen A. Khan, Ahmed Elshahhat. Analysis of Weibull progressively first-failure censored data with beta-binomial removals[J]. AIMS Mathematics, 2024, 9(9): 24109-24142. doi: 10.3934/math.20241172

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Abstract

This study examined the estimations of Weibull distribution using progressively first-failure censored data, under the assumption that removals follow the beta-binomial distribution. Classical and Bayesian approaches for estimating unknown model parameters have been established. The estimations included scale and shape parameters, reliability and failure rate metrics as well as beta-binomial parameters. Estimations were considered from both point and interval viewpoints. The Bayes estimates were developed by using the squared error loss and generating samples for the posterior distribution through the Markov Chain Monte Carlo technique. Two interval estimation approaches are considered: approximate confidence intervals based on asymptotic normality of likelihood estimates and Bayes credible intervals. To investigate the performance of classical and Bayesian estimations, a simulation study was considered by various kinds of experimental settings. Furthermore, two examples related to real datasets were thoroughly investigated to verify the practical importance of the suggested methodologies.

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