Comparative study of the dependence effect on competing risks models with three modes of failure via estimators copula based

Abstract

In a dependent competing risks model is impossible to determine the marginal distributions from the competing risks data alone. This is known as the identifiability problem.  Zheng and Klein (1995) propose the copula graphic estimator as a solution to the identifiability problem for two competing risks. For that, they assume a dependence structure using a copula for the joint distribution of failure times and its dependence parameter known. Lo and Wilke (2010) propose the risk pooling method as an extension of the copula graphic estimator when the copula is  Archimedean.  This  research  for  the  trivariate  case,  is  compared  the  true  joint  survival  function,  with  joint  survival function estimated assuming independence among failure times and the survival function estimated by the risk pooling method. These comparisons are performed via simulation considering failure times associated with  multivariate  Weibull  and  lognormal  distributions  and  different  levels  of  dependence  between  failure  times. We conclude that the estimator assuming independence is less efficient than the estimator of the survival function using the risk pooling method. The methodology is illustrated with reliability data of FL245 switches in Interconexión Eléctrica S.A. E.S.P. (ISA), which show the usefulness of this topic in industrial reliability.