Accelerated Life Testing for Bivariate Distributions based on Progressive Censored Samples with Random Removal

Authors

El-Sayed A. El-Sherpieny, Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, EgyptFollow
Hiba Z. Muhammed, Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, EgyptFollow
Ehab M. Almetwally, Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt\\ Department of Statistics, Faculty of Business Administration, Delta University for Science and Technology, Gamasa, 11152, EgyptFollow

Abstract

The significance of the statistical inference problem in reliability theory for the bivariate models under accelerated life testing (ALT) is enormous. In practice, independent variables are assumed for the sake of convenience, which contradicts the nature of the problem. The constant stress accelerated life testing (CS-ALT) for the bivariate model based on copula function is introduced in this study. The copula is the method that describes the dependence structure between variables. The model parameters are evaluated using maximum likelihood and Bayesian estimation methods, taking into account that units fail due to only two dependent variables under continuous stress ALTs and a Type-II progressive censoring scheme. For the bivariate model, random removal has been referred to as binomial removal. The Bayesian estimation has been created using symmetric and asymmetric loss functions. The asymptotic confidence intervals are generated using approximated confidence intervals. Interval Bayesian estimators have been employed with credible confidence intervals. The set of simulated data is evaluated for demonstrative reasons, taking into account two and numerous stress levels. Different Monto Carlo simulations are built to compare estimating approaches.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/jsap/110228

Recommended Citation

A. El-Sherpieny, El-Sayed; Z. Muhammed, Hiba; and M. Almetwally, Ehab (2022) "Accelerated Life Testing for Bivariate Distributions based on Progressive Censored Samples with Random Removal," Journal of Statistics Applications & Probability: Vol. 11: Iss. 2, Article 28.
DOI: http://dx.doi.org/10.18576/jsap/110228
Available at: https://digitalcommons.aaru.edu.jo/jsap/vol11/iss2/28