This article aims at the lifetime prognosis of one-shot devices subject to competing causes of failure. Based on the failure count data recorded across several inspection times, statistical inference of the lifetime distribution is studied under the assumption of Lindley distribution. In the presence of outliers in the data set, the conventional maximum likelihood method or Bayesian estimation may fail to provide a good estimate. Therefore, robust estimation based on the weighted minimum density power divergence method is applied both in classical and Bayesian frameworks. Thereafter, the robustness behaviour of the estimators is studied through influence function analysis. Further, in density power divergence based estimation, we propose an optimization criterion for finding the tuning parameter which brings a trade-off between robustness and efficiency in estimation. The article also analyses when the cause of failure is missing for some of the devices. The analytical development has been restudied through a simulation study and a real data analysis where the data is extracted from the SEER database.

翻译：本文旨在研究面临竞争失效原因的一次性设备的寿命预后。基于多个检测时间点记录的失效计数数据，在Lindley分布假设下对寿命分布进行统计推断。当数据集中存在异常值时，传统的极大似然方法或贝叶斯估计可能无法提供良好的估计值。因此，本文在经典和贝叶斯框架下均采用基于加权最小密度幂散度方法的稳健估计。随后，通过影响函数分析研究估计量的稳健性行为。此外，在基于密度幂散度的估计中，我们提出了一种优化准则，用于寻找能平衡估计稳健性与效率的调节参数。本文还分析了部分设备失效原因缺失的情况。通过模拟研究和从SEER数据库提取的真实数据分析，对分析方法的有效性进行了重新验证。