A Competing Risks Model With Multiply Censored Reliability Data Under Multivariate Weibull Distributions

Abstract

A competing risks model is composed of more than one failure mode that naturally arises when reliability systems are made of two or more components. A series system fails if any of its components fail. As these components are all part of the same system, they may be correlated. In this paper, we consider a competing risks model with $k$ failure modes and whose lifetimes follow a joint $k$ -variate Marshall–Olkin Weibull distribution, when the data are multiply censored. Normally, each observation contains the failure time as well as the failure mode. In practice, however, it is common to have masked data in which the component that causes failure of the system is not observed. We apply the maximum likelihood approach via expectation–maximization algorithm, along with the missing information principle, to estimate the parameters and the standard errors of the maximum likelihood estimates. Statistical inference on the model parameters, the mean time to failure, and the quantiles of the failure time of the system as well as of the components are all developed. The proposed method is evaluated by a simulation study and also applied to two two-component real datasets successfully.