Statistical inference for multicomponent stress-strength reliability for the Perk distribution under adaptive type-I progressive hybrid censoring

This study develops a reliability framework for multicomponent stress-strength models based on the Perk distribution, a flexible choice for limited lifetime data. To mirror the practical time and resource limits of industrial testing, we adopt an adaptive Type-I progressive hybrid censoring scheme. We derive a range of frequentist estimators—including maximum likelihood and maximum product of spacings—and contrast them with a Bayesian approach designed to handle complex posteriors via the Metropolis–Hastings algorithm. Crucially, this model provides a mathematical basis for evaluating environmental resilience, where system reliability represents the capacity of an ecosystem to withstand stressors like pollution, climate variability, and extreme weather. Our simulations reveal that Bayesian methods, particularly under asymmetric loss, offer superior precision in small or highly censored samples, while classical methods remain efficient as sample sizes grow. The framework’s utility is finally demonstrated through an application to composite material strengths, offering a practical guide for analyzing complex reliability configurations in environmental science.