Inferences and Engineering Applications of Alpha Power Weibull Distribution Using Progressive Type-II Censoring

Refah Alotaibi, Mazen Nassar, Hoda Rezk and Ahmed Elshahhat ()
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Refah Alotaibi: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Mazen Nassar: Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Hoda Rezk: Department of Statistics, Al-Azhar University, Cairo 11751, Egypt
Ahmed Elshahhat: Faculty of Technology and Development, Zagazig University, Zagazig 44519, Egypt

Mathematics, 2022, vol. 10, issue 16, 1-21

Abstract: As an extension of the standard Weibull distribution, a new crucial distribution termed alpha power Weibull distribution has been presented. It can model decreasing, increasing, bathtub, and upside-down bathtub failure rates. This research investigates the estimation of model parameters and some of its reliability characteristics using progressively Type-II censored data. To get estimates of unknown parameters, reliability, and hazard rate functions, the maximum likelihood, and Bayesian estimation approaches are studied. To acquire estimated confidence intervals for unknown parameters and reliability characteristics, the maximum likelihood asymptotic properties are used. The Markov chain Monte Carlo approach is used in Bayesian estimation to provide Bayesian estimates under squared error and LINEX loss functions. Furthermore, the highest posterior density credible intervals of the parameters and reliability characteristics are determined. A Monte Carlo simulation study is used to investigate the accuracy of various point and interval estimators. In addition, various optimality criteria are used to choose the best progressive censoring schemes. Two real data from the engineering field are analyzed to demonstrate the applicability and significance of the proposed approaches. Based on numerical results, the Bayesian procedure for estimating the parameters and reliability characteristics of alpha power Weibull distribution is recommended. The analysis of two real data sets showed that the alpha power Weibull distribution is a good model to investigate engineering data in the presence of progressive Type-II censoring.

Keywords: alpha power weibull distribution; progressive Type-II censoring; maximum likelihood; Bayesian paradigm; reliability measures; MCMC techniques (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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