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.

翻译：一次性设备的可靠性预测因其广泛的应用性而日益受到关注。本研究旨在基于步进应力加速寿命试验（SSALT）并应用累积风险模型（CRM），对高耐久性一次性设备单元的寿命进行预测。在SSALT实验中，CRM通过允许应力变化效应出现前的滞后阶段来保持风险函数的连续性。在对此类寿命数据的分析中，大量数据集可能包含异常值，而最大似然估计或基于似然的贝叶斯估计等传统方法经常失效。本文开发了一种基于密度幂散度的鲁棒估计方法，涵盖经典框架和贝叶斯框架。通过基于鲁棒化后验的贝叶斯因子进行假设检验。在贝叶斯估计中，我们利用哈密顿蒙特卡洛方法，该方法相比传统的Metropolis-Hastings算法具有一定优势。进一步，通过分析影响函数评估估计量和贝叶斯因子的鲁棒性。最后，通过模拟研究和实际数据分析验证了理论推导的有效性。