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

TL;DR

This paper develops a robust method for estimating dependent competing risks in lifetime data with interval monitoring, introduces an optimal inspection schedule, and employs genetic algorithms for design optimization.

Contribution

It proposes a divergence-based robust estimation approach for dependent competing risks modeled by Marshal-Olkin distribution and determines optimal inspection intervals using multiobjective genetic algorithms.

Findings

Robust point estimators with derived influence functions.

Effective hypothesis testing via Wald type tests.

Optimal inspection schedules based on multi-criteria optimization.

Abstract

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.