Non-parametric estimation of the availability in a general repairable system

This work deals with repairable systems with unknown failure and repair time distributions. We focus on the estimation of the instantaneous availability, that is, the probability that the system is functioning at a given time, which we consider as the most significant measure for evaluating the effectiveness of a repairable system.The estimation of the availability function is not, in general, an easy task, i.e., analytical techniques are difficult to apply. We propose a smooth estimation of the availability based on kernel estimator of the cumulative distribution functions (CDF) of the failure and repair times, for which the bandwidth parameters are obtained by bootstrap procedures. The consistency properties of the availability estimator are established by using techniques based on the Laplace transform.