Robust Bayesian inference for nondestructive one-shot device testing data under competing risk using Hamiltonian Monte Carlo method

The prevalence of one-shot devices is quite prolific in engineering and medical domains. Unlike typical one-shot devices, nondestructive one-shot devices (NOSD) may survive multiple tests and offer additional data for reliability estimation. This study aims to implement the Bayesian approach to the lifetime prognosis of NOSD when failures are subject to multiple risks. With small deviations from the assumed model conditions, conventional likelihood-based Bayesian estimation may result in misleading statistical inference, raising the need for a robust Bayesian method. This work develops Bayesian estimation by exploiting a robustified posterior based on the density power divergence measure for NOSD test data. Further, the testing of the hypothesis is carried out by applying a proposed Bayes factor derived from the robustified posterior. A flexible Hamiltonian Monte Carlo approach is applied to generate posterior samples. Additionally, we assess the extent of resistance of the proposed methods to small deviations from the assumed model conditions by applying the influence function (IF) approach. In testing of hypothesis, IF reflects how outliers impact the decision-making through Bayes factor under null hypothesis. Finally, this analytical development is validated through a simulation study and a data analysis based on cancer data.