Reliability assessment of consecutive k-out-of-n:G system: stress-strength analysis under a class of distributions

In this paper, we investigate the reliability evaluation of a consecutive k-out-of-n:G system within the stress–strength framework. The analysis is conducted under a class of distributions known as the proportional reversed hazard rate family, which generalizes several well-known lifetime distributions. Both classical and Bayesian approaches are employed to estimate system reliability and to assess the influence of the model parameter on system performance. Maximum likelihood and Bayesian estimation methods are used in parallel, and asymptotic confidence intervals as well as highest posterior density credible intervals are derived to quantify estimation uncertainty. A simulation study and a real data analysis based on the flexible exponentiated Burr–Hatke distribution—a recently introduced member of the PRHR family—are provided to demonstrate the efficacy and practical relevance of the proposed methods.