The Marshall–Olkin Power Half-Logistic Distribution for Reliability Modeling of Degradation Data Under Generalized Hybrid Censoring

Abstract

The prediction of material lifetime is central to nanomaterial engineering and reliability analysis. We propose the Marshall–Olkin Power Half-Logistic (MOPHL) distribution, obtained by applying a Marshall–Olkin transform to the Power Half-Logistic baseline. We derive core properties—including moments, hazard rate characterization, and Rényi entropy—and develop inference under generalized progressive hybrid censoring. Estimation is carried out via maximum likelihood and Bayesian methods using a Metropolis–Hastings sampler. Asymptotic results, Fisher information, and corresponding confidence/credible intervals are provided. A Monte Carlo study assesses bias, the mean squared error, and coverage across censoring scenarios and hazard regimes. In a case study on hydroxylated fullerene degradation, MOPHL outperforms nine competing models in goodness-of-fit and predictive reliability. We also report the mean time to failure and mean residual life to support engineering decision-making. The proposed framework offers a tractable and robust tool for degradation analysis under censored data, with applicability to materials, mechanical components, biomedical devices, and environmental monitoring.