A finite mixture model for multiple dependent competing risks with applications of automotive warranty claims data

This paper introduces a parametric finite mixture model (FMM) approach to analyze the dependent competing risks data subjected to progressive first-failure censoring and multiple causes of failure. The cause-specific failure times are assumed to be flexibly modeled by the Lehmann family of distributions (also known as the exponentiated distributions) with variation in both distribution parameters. Application of the expectation maximization (EM) algorithm facilitates the maximum likelihood estimation of the model parameters and illuminates the contribution of the censored data. For interval estimation purposes, we resort to using the asymptotic confidence intervals based on the observed Fisher information matrix. Practitioners often prefer employing simpler lifetime distribution in order to facilitate the data modeling process while knowing the true distribution. In this context, the effects of model misspecification are studied based on the p-th quantile when the true distribution is misspecified. An extensive simulation study is performed to validate our proposed model. Finally, an automotive warranty claims data set is used as an illustration to study the effectiveness of our proposed model, assuming some important members of the Lehmann family, like generalized exponential and exponentiated Pareto distributions.