Statistical Inference for the Jointly Adaptive Progressive Type-II Censored Weibull Distributions

In a life-testing experiment, the joint progressive censoring scheme for more than one exponential population was proposed by Rasouli and Balakrishnan (Commun Stat Theory Methods 39(12):2172–2191, 2010). In this paper, we focus on the joint adaptive progressive Type-II (JAPC-II) censoring scheme for two populations to reduce the experimental time as well as cost of the experiment. The methodology is developed for the Weibull distribution with common shape parameter β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document} and different scale parameters α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} and λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}, respectively. We consider the maximum likelihood estimators of the unknown scale and shape parameters along with their asymptotic and bootstrap confidence intervals. Further, the Bayesian inference procedure is provided with the corresponding credible intervals. Theoretical studies are illustrated based on simulation study. We also provide some connection between our proposed model with the balanced joint adaptive progressive censoring scheme, proposed by Sultana et al. (Statistics 55(6):1328–1355, 2021). Finally, the methods are illustrated with the analysis of a real data set.