Inferential analysis of the stress-strength reliability for a new extended family of distributions

This study addresses the estimation of system reliability, denoted as [Formula: see text], where X and Y are independent but not identically distributed random variables from an extended distribution family, incorporating a new parameter to extend the normal and Weibull distributions. We propose estimators, including the maximum likelihood and Bayes estimators, as well as various confidence and credible intervals for both the unknown parameters and R, utilizing conjugate priors. In a Bayesian context, we use importance sampling within the Metropolis-Hastings sampler for parameter and reliability function estimation. Additionally, the effectiveness of our proposed methods is performed through the analysis of real-world data and comprehensive numerical simulations.