A Robust Bayesian approach for reliability prognosis of one-shot devices under cumulative risk model

The reliability prognosis of one-shot devices is drawing increasing attention because of their wide applicability. The present study aims to determine the lifetime prognosis of highly durable one-shot device units under a step-stress accelerated life testing (SSALT) experiment applying a cumulative risk model (CRM). In an SSALT experiment, CRM retains the continuity of hazard function by allowing the lag period before the effects of stress change emerge. In an analysis of such lifetime data, plentiful datasets might have outliers where conventional methods like maximum likelihood estimation or likelihood-based Bayesian estimation frequently fail. This work develops a robust estimation method based on density power divergence in classical and Bayesian frameworks. The hypothesis is tested by implementing the Bayes factor based on a robustified posterior. In Bayesian estimation, we exploit Hamiltonian Monte Carlo, which has certain advantages over the conventional Metropolis-Hastings algorithms. Further, the influence functions are examined to evaluate the robust behaviour of the estimators and the Bayes factor. Finally, the analytical development is validated through a simulation study and a real data analysis.