Survival Analysis of the PRC Model from Adaptive Progressively Hybrid Type-II Censoring and Its Engineering Applications

Ahmed Elshahhat (), Osama E. Abo-Kasem and Heba S. Mohammed
Additional contact information
Ahmed Elshahhat: Faculty of Technology and Development, Zagazig University, Zagazig 44519, Egypt
Osama E. Abo-Kasem: Department of Statistics, Faculty of Commerce, Zagazig University, Zagazig 44519, Egypt
Heba S. Mohammed: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

Mathematics, 2023, vol. 11, issue 14, 1-26

Abstract: A new two-parameter statistical model, obtained by compounding the generalized-exponential and exponential distributions, called the PRC lifetime model, is explored in this paper. This model can be easily linked to other well-known six-lifetime models; namely the exponential, log-logistic, Burr, Pareto and generalized Pareto models. Adaptive progressively hybrid Type-II censored strategy, used to increase the efficiency of statistical inferential results and save the total duration of a test, has become widely used in various sectors such as medicine, biology, engineering, etc. Via maximum likelihood and Bayes inferential methodologies, given the presence of such censored data, the challenge of estimating the unknown parameters and some reliability time features, such as reliability and failure rate functions, of the PRC model is examined. The Markov-Chain Monte Carlo sampler, when the model parameters are assumed to have independent gamma density priors, is utilized to produce the Bayes’ infer under the symmetric (squared-error) loss of all unknown subjects. Asymptotic confidence intervals as well as the highest posterior density intervals of the unknown parameters and the unknown reliability indices are also created. An extensive Monte Carlo simulation is implemented to investigate the accuracy of the acquired point and interval estimators. Four various optimality criteria, to select the best progressive censored design, are used. To demonstrate the applicability and feasibility of the proposed model in a real-world scenario, two data sets from the engineering sector; one based on industrial devices and the other on aircraft windshield, are analyzed. Numerical evaluations showed that the PRC model furnishes a superior fit compared to seven other models in the literature, including: alpha-power exponential, log-logistic, Nadarajah–Haghighi, generalized-exponential, Weibull, gamma and exponential lifetime distributions. The findings demonstrate that, in order to obtain the necessary estimators, the Bayes’ paradigm via Metropolis–Hastings sampler is recommended compared to its competitive likelihood approach.

Keywords: PRC model; adaptive progressively hybrid type-II censoring; symmetric Bayes inference; maximum likelihood; Metropolis–Hastings algorithm; reliability; optimum design (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/14/3124/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/14/3124/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:14:p:3124-:d:1194598

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().