Estimation in a General Repair Model Based on Left-truncated Data

We consider a repairable system with general repairs introduced by Last & Szekli (1998a ). Apart from simple special cases this model leads to a strong dependency among the observed failure times. Our aim is to estimate the underlying failure time distribution and its cumulative hazard given that the failure process has been observed up to the n th failure. We use non-parametric estimators of Kaplan–Meier and Nelson–Aalen type. We prove strong uniform consistency of the estimators as n tends to infinity. Further results on weak convergence are derived. Neither stationarity nor mixing conditions are required.