Reliability analysis in stress-strength model under record values with practical verification

Abstract

This article uses upper record values to estimate the stress-strength reliability parameter, defined as $$\dddot \delta = P(Z < T).$$ We assume that both strength (T) and stress (Z) are independent random variables that follow the inverted exponentiated Pareto distribution with a common second shape parameter. The maximum likelihood and Bayesian estimators of $$\dddot \delta$$are obtained. Using informative and non-informative priors, the Bayesian estimators are obtained under symmetric and asymmetric loss functions. Two bootstrap-type confidence intervals and highest posterior credible intervals are constructed. Gibbs and Metropolis-Hasting samplers are used to generate Bayesian estimates of reliability $$\dddot \delta$$ based on the suggested loss functions. To investigate the behavior of suggested approaches, extensive simulation studies are carried out using some accuracy measures. Simulation experiment findings validated the consistency of the Bayesian and non-Bayesian estimates of $$\dddot \delta .$$ According to specific metrics, Bayesian estimates under symmetric loss function showed more precision than those under asymmetric loss functions. The lengths of credible intervals for Bayesian estimates are less than the bootstrap confidence intervals for different record numbers. The bootstrap-p confidence intervals give more accurate outcomes than bootstrap-t in most cases. The analysis employs two representative datasets. The first includes the timing of goals scored in the final rounds of the European Champions League over two consecutive seasons. The second dataset contains monthly observations of sulfur dioxide concentration in Long Beach, California, spanning the years 1956 to 1974.