Nonparametric estimation of some important indicators in reliability for semi-Markov processes

In this article we present nonparametric estimators of the mean time to failure (MTTF), the mean up time (MUT), and the mean down time (MDT) of an arbitrary finite semi-Markov process. Strong consistency and weak convergence is proved for the estimators of MTTF, MUT, and MDT, as the time interval of observation becomes large.