Stress–strength reliability models are essential for assessing the safety and performance of engineering systems operating under uncertainty and censored lifetime data. This paper develops a reliability framework for multicomponent stress–strength systems by modeling stress and strength using the Burr–Hatke distribution under progressive Type II censoring. Maximum likelihood estimators are derived for the model's parameters and the stress–strength reliability function, along with their asymptotic confidence intervals. To improve finite–sample inference, bootstrap confidence intervals are constructed. Bayesian estimation is performed under a generalized entropy loss function using gamma priors, using Lindley's approximation and Markov chain Monte Carlo techniques. The corresponding credible intervals and highest posterior density intervals are obtained for interval estimation. Extensive Monte Carlo simulations and applications to rear dump truck failure times and earthquake inter–event data demonstrate the effectiveness and robustness of the proposed approach under progressive censoring.