Some remarks on dependent censoring in complex systems

We consider a sample of independent binary complex systems, all having the same structure. Each system is continuously observed until it fails. The failure time of a component is observed and recorded if the component fails before the system does. If a component is still functioning at the time of system failure, its lifelength cannot be observed and the time of system failure is recorded as censoring time instead. Based on these failure and censoring times, Doss, Freitag and Proschan (1989) introduced an estimator of the distribution of the system lifelength in the case that the components of the system are independent. In this paper we discuss possibilities to weaken the assumption of independent component lifelengths. Under these weaker assumptions we introduce methods of estimating the distribution functions of the system lifelength and the component lifelengths.