Robust estimation of dependent competing risk model under interval monitoring and determining optimal inspection intervals

Recently, a growing interest is evident in modelling dependent competing risks in lifetime prognosis problems. In this work, we propose to model the dependent competing risks by Marshal-Olkin bivariate exponential distribution. The observable data consists of a number of failures due to different causes across different time intervals. The failure count data is common in instances like one-shot devices where the state of the subjects is inspected at different inspection times rather than the exact failure times. The point estimation of the lifetime distribution in the presence of competing risk has been studied through a divergence-based robust estimation method called minimum density power divergence estimation (MDPDE) with and without constraint. The optimal value of the tuning parameter has been obtained. The testing of the hypothesis is performed based on a Wald-type test statistic. The influence function is derived for the point estimator and the test statistic, reflecting the degree of robustness. Another key contribution of this work is determining the optimal inspection times based on predefined objectives. This article presents the determination of multi-criteria-based optimal design. Population-based heuristic algorithm nondominated sorting-based multiobjective Genetic algorithm is exploited to solve this optimization problem.