  Recently, a growing amount interest is quite evident in modelling dependent
competing risks in life time prognosis problem. In this work, we propose to
model the dependent competing risks by Marshal-Olkin bivariate exponential
distribution. The observable data consists of number of failures due to
different causes across different time intervals. The failure count data is
common in instances like one shot devices where state of the subjects are
inspected at different inspection times rather than the exact failure times.
The point estimation of the life time distribution in presence of competing
risk has been studied through divergence based robust estimation method called
minimum density power divergence estimation (MDPDE). The testing of hypothesis
is performed based on a Wald type test statistic. The influence function is
derived both for the point estimator and the test statistic, which reflects the
degree of robustness. Another, key contribution of this work is to determine
the optimal set of inspection times based on some predefined objectives. This
article presents determination of multi criteria based optimal design.
Population based heuristic algorithm non-dominated sorting-based multiobjective
Genetic algorithm is exploited to solve this optimization problem.
