stress-strength reliability of the proportional hazard rate models under type-i progressively hybrid censored samples

This study focuses on estimating the stress-strength parameter r‎, ‎utilizing two independent type-i progressively hybrid censored samples derived from populations governed by the proportional hazard rate model‎. ‎the maximum likelihood and bayes estimators are obtained under some well-known loss functions and the assumption that the priors are independently gamma-distributed‎. ‎the asymptotic confidence interval and bayesian and highest posterior density credible intervals are also presented‎. ‎a monte carlo simulation study is used to evaluate the performances of the obtained point estimators and confidence and credible intervals‎. ‎finally‎, ‎a pair of real data sets is analyzed for illustrative purposes.