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

TL;DR

This paper introduces a robust Bayesian framework using Hamiltonian Monte Carlo for reliability analysis of nondestructive one-shot devices under competing risks, effectively handling small deviations from model assumptions.

Contribution

It develops a robust Bayesian estimation method based on density power divergence and introduces a Bayes factor for hypothesis testing in NOSD data, validated through simulations and real data.

Findings

Robust Bayesian estimates are less sensitive to model deviations.

The proposed Bayes factor effectively detects outliers and model misspecifications.

Simulation and real data confirm the method's reliability and robustness.

Abstract

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 of 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.