Abstract

Mathematical modeling of degradation data is essential for quantifying the lifetime, reliability, and long-term stability of advanced materials when a direct experimental assessment is costly or limited. This paper develops an applied statistical framework based on the proportional hazard Gumbel Type-II (PHGT-II) distribution for modeling positive degradation times under a generalized progressive hybrid censoring scheme. The proposed model extends the baseline Gumbel Type-II distribution through a proportional hazard structure, providing additional flexibility for representing non-monotone hazard behavior, heavy-tailed lifetime patterns, and heterogeneous degradation mechanisms. The probability density, survival, hazard, and mean time to failure functions were derived, and the likelihood function was formulated under generalized progressive hybrid censoring. Parameter estimation was performed using maximum likelihood estimation and Bayesian inference with independent Gamma priors. Bayesian estimates were obtained under squared error and general entropy loss functions using a Metropolis–Hastings algorithm. The model was applied to thermal degradation data of the hydroxylated fullerene nanocomposite Sc3N@C80(OH)18, where the degradation time was defined through a 2% weight-loss threshold obtained from a thermogravimetric analysis. The PHGT-II model was compared with other distributions using several goodness-of-fit measures. The results show that the PHGT-II distribution provides the best fit to the observed degradation data and yields consistent reliability estimates across maximum likelihood and Bayesian approaches. The proposed framework offers a flexible and interpretable tool for modeling censored degradation data and can be extended to other reliability and lifetime applications in engineering and material science.

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