Reliability inference for Lomax distribution under block progressive type-II censoring

The Lomax distribution and block censoring schemes play a significant role in life testing and reliability engineering, enabling researchers to model lifetime data more accurately and conduct tests more efficiently. Block censoring, in particular, enhances resource management by allowing a fixed number of test units to be assigned to different facilities, making the testing process more structured and practical. In this paper, we propose a hierarchical Bayesian model for estimating key reliability measures including the reliability function, hazard rate and mean time to failure (MTTF) while also accounting for potential differences across test environments. The model assumes that unit lifetimes follow Lomax distribution. We demonstrate how this framework can be applied to estimate reliability metrics and assess its performance by comparing the proposed Bayesian method to the traditional maximum likelihood estimation (MLE) through extensive simulation studies. The existence and uniqueness of maximum likelihood estimators of model parameters are established, and approximate confidence intervals are obtained. The results indicate that the hierarchical Bayesian model, which incorporates non-informative priors and employs a hybrid Metropolis-Hastings sampling algorithm, outperforms the nonhierarchical MLE approach. Finally, the practical utility of the model is illustrated using two real-world reliability datasets.