Stress-strength reliability inference in multicomponent systems under the unit-gamma Gompertz–Weibull distribution based on progressive Type-II censoring

Reliable assessment of multicomponent systems operating under uncertain stress is fundamental to modern engineering, environmental management, and risk analysis. In many practical life-testing experiments, observations are subject to progressive Type-II censoring, and system capacities are naturally bounded, rendering classical stress-strength models inadequate for capturing complex reliability behaviour. Despite extensive developments in parametric reliability modeling, flexible frameworks capable of jointly accommodating multicomponent system structures, bounded distributions, and progressive censoring remain limited. This study develops a comprehensive inferential framework for multicomponent stress-strength reliability under progressive Type-II censoring based on the Unit-Gamma Gompertz-Weibull distribution. The proposed model provides substantial flexibility in modeling diverse density and hazard-rate shapes while preserving analytical tractability for reliability formulation. We derive explicit expressions for key reliability measures and construct a unified estimation strategy that integrates maximum likelihood estimation, approximate likelihood methods, a Monte Carlo expectation-maximization algorithm, and Bayesian inference via Lindley's approximation and Metropolis-Hastings sampling. Extensive Monte Carlo simulations demonstrate stable finite-sample performance across varying censoring intensities and system configurations. Application to hydrological capacity data from the Shasta reservoir highlights improved goodness-of-fit and more robust reliability estimation compared with competing bounded distributions. Sensitivity and influence analyses further confirm the stability of the proposed framework. Overall, the methodology offers a flexible and practically implementable tool for stress-strength reliability analysis in multicomponent systems with censored and bounded observations.