Multicomponent stress-strength reliability analysis using the inverted exponentiated Rayleigh distribution under block adaptive type-II progressive hybrid censoring and k-records

We propose a statistical model for multicomponent stress-strength reliability under the inverted exponentiated Rayleigh distribution. The model is specifically designed for complex data structures where component strength is measured using block adaptive Type-II progressive hybrid censoring, while operational stress is captured as upper k-records with inter-k-record times. After formulating the reliability function for an s-out-of-k system, we develop both frequentist and Bayesian estimation procedures. Frequentist inference is based on the maximum likelihood estimator, from which we construct asymptotic and bootstrap confidence intervals. For the Bayesian analysis, we use squared error and linear exponential loss functions, obtaining estimates via the Tierney and Kadane approximation and a Metropolis-Hastings sampling algorithm. The performance of the estimators is evaluated through Monte Carlo simulations, which compare their bias and mean squared error. The results indicate that the Bayesian estimators are consistently more accurate than their frequentist counterparts. An analysis of two real datasets confirms the model's practical utility for assessing system reliability in complex scenarios.