Nonparametric reliability estimation of semi-Markov processes

We define estimators of reliability and availability of such systems and show that they are uniformly strongly consistent and that each of them converges weakly to a normal random variable. The result of Baxter and Li (Scand. J. Statist. 21 (1994) 277) for an alternated renewal process appears as a particular case of our result. A method for constructing confidence intervals is also given. This is made possible by use of recent results of Ouhbi and Limnios (Appl. Stochast. Mod. Data Anal. 12 (4) (1996) 209; C. R. Acad. Sci. Paris 325 (1997) 921) establishing asymptotic properties of the estimators of the semi-Markov kernel and the Markov renewal matrix, respectively.