The present study aims to determine the lifetime prognosis of highly durable nondestructive one-shot devices (NOSD) 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. When prior information about the model parameters is available, Bayesian inference is crucial. In a Bayesian analysis of such lifetime data, conventional likelihood-based Bayesian estimation frequently fails in the presence of outliers in the dataset. This work incorporates a robust Bayesian approach utilizing a robustified posterior based on the density power divergence measure. The order restriction on shape parameters has been incorporated as a prior assumption to reflect the decreasing expected lifetime with increasing stress levels. In testing of hypothesis, a Bayes factor is implemented based on the 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：本研究旨在通过应用累积风险模型（CRM）的步进应力加速寿命试验（SSALT），确定高耐久性非破坏性一次性设备（NOSD）单元的寿命预测。在SSALT实验中，CRM通过允许应力变化效应显现前的滞后阶段，保持了风险函数的连续性。当模型参数的先验信息可用时，贝叶斯推断至关重要。在此类寿命数据的贝叶斯分析中，基于传统似然的贝叶斯估计在数据集中存在异常值时经常失效。本研究采用了一种稳健的贝叶斯方法，该方法利用基于密度功率散度度量的稳健化后验分布。形状参数的顺序限制已作为先验假设纳入，以反映预期寿命随应力水平增加而降低的特性。在假设检验中，基于稳健化后验实现了贝叶斯因子的计算。在贝叶斯估计中，我们采用了哈密顿蒙特卡洛方法，该方法相较于传统的Metropolis-Hastings算法具有特定优势。此外，通过考察影响函数来评估估计量与贝叶斯因子的稳健性。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。