Estimation of multicomponent system reliability for inverse Weibull distribution using survival signature

The problem of estimating multicomponent stress-strength reliability Rk,n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{k,n}$$\end{document} for two-parameter inverse Weibull distributions under progressive type-II censoring is considered. We derive maximum likelihood estimator, Bayes estimator and generalised confidence interval of Rk,n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{k,n}$$\end{document} when all parameters are unknown. We study the reliability of stress-strength system with multiple types of components using signature-based approach. When different types of random stresses are acting on a compound system, we derive MLE, maximum spacing estimator of multi-state reliability. Using generalized pivotal quantity, the generalized confidence interval and percentile bootstrap intervals of the reliability are derived. Under a common stress subjected to the system, we also derive the estimators of the reliability parameter. Different point estimators and generalized, bootstrap confidence intervals of the reliability are developed. Risk comparison of the classical and Bayes estimators is carried out using Monte-Carlo simulation. Application of the proposed estimators is shown using real-life data sets.