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 fundamentalto modern engineering, environmental management, and risk analysis. In many practicallife-testing experiments, observations are subject to progressive Type-II censoring, andsystem capacities are naturally bounded, rendering classical stress–strength models inadequatefor capturing complex reliability behaviour. Despite extensive developments in parametric reliabilitymodeling, flexible frameworks capable of jointly accommodating multicomponent systemstructures, bounded distributions, and progressive censoring remain limited. This studydevelops a comprehensive inferential framework for multicomponent stress–strength reliabilityunder progressive Type-II censoring based on the Unit-Gamma Gompertz–Weibull distribution.The proposed model provides substantial flexibility in modeling diverse density andhazard-rate shapes while preserving analytical tractability for reliability formulation. We deriveexplicit expressions for key reliability measures and construct a unified estimation strategythat integrates maximum likelihood estimation, approximate likelihood methods, a Monte Carloexpectation–maximization algorithm, and Bayesian inference via Lindley’s approximation andMetropolis–Hastings sampling. Extensive Monte Carlo simulations demonstrate stable finitesampleperformance across varying censoring intensities and system configurations. Applicationto hydrological capacity data from the Shasta reservoir highlights improved goodness-of-fit andmore robust reliability estimation compared with competing bounded distributions. Sensitivityand influence analyses further confirm the stability of the proposed framework. Overall, themethodology offers a flexible and practically implementable tool for stress–strength reliabilityanalysis in multicomponent systems with censored and bounded observations. AMS 2000 Subject Classification: Primary 62N05; Secondary 62F10.