Parametric Inference for a Multicomponent Stress–Strength Reliability Model With Kumaraswamy Distribution Under Ordered Ranked Set Sampling

Assessing reliability in systems with dual stress constraints needs a flexible model and effective sampling methods. A framework using the Kumaraswamy distribution is set up for multicomponent stress and strength systems. Data collection is done through ordered ranked set sampling, leveraging the unified theory of generalized order statistics to optimize information gathering and handle varying sample sizes. Maximum likelihood estimators are calculated for model parameters and reliability, with interval estimates obtained using different techniques like asymptotic normality and bootstrap. A key advancement is an empirical Bayesian approach with balanced loss functions to fine-tune estimators for both symmetric and asymmetric risk. To enhance reliability, the highest posterior density intervals are developed. The framework is tested through simulations and applied to real data, proving it to be a robust and efficient method for evaluating structural reliability.