Analysis of stress-strength reliability for multicomponent system from Rayleigh model with a hybrid censored data

This study evaluates multicomponent stress-strength system reliability (MSR) using data from adaptive Type-II hybrid progressive censoring. For strength and stress variables following two-parameter Rayleigh models with shared parameters, maximum likelihood estimation is derived for the MSR quantity, where the existence and uniqueness of the likelihood estimators are also established for model parameters. Approximate confidence interval for MSR is developed based on asymptotic theory and delta method. For comparative analysis, generalised estimation methods are proposed based on proposed pivotal quantities, and alternative point estimates and confidence intervals are constructed in consequence. The methodology is further extended to case with fully unequal parameters, both classical and generalised estimations are conducted as well. Additionally, a likelihood ratio testing framework is provided to verify parameter equivalence between strength and stress variables. The performance of different estimation methods is evaluated via Monte Carlo simulations, and a real-life example is also conducted for applications.