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This article aims at the lifetime prognosis of one-shot devices subject tocompeting causes of failure. Based on the failure count data recorded acrossseveral inspection times, statistical inference of the lifetime distribution isstudied under the assumption of Lindley distribution. In the presence ofoutliers in the data set, the conventional maximum likelihood method orBayesian estimation may fail to provide a good estimate. Therefore, robustestimation based on the weighted minimum density power divergence method isapplied both in classical and Bayesian frameworks. Thereafter, the robustnessbehaviour of the estimators is studied through influence function analysis.Further, in density power divergence based estimation, we propose anoptimization criterion for finding the tuning parameter which brings atrade-off between robustness and efficiency in estimation. The article alsoanalyses when the cause of failure is missing for some of the devices. Theanalytical development has been restudied through a simulation study and a realdata analysis where the data is extracted from the SEER database.

Robust Inference of One-Shot Device testing data with Competing Risk  under Lindley Lifetime Distribution with an application to SEER Pancreas  Cancer Data