Non-parametric estimation of lifetime and repair time criteria for a semi-Markov process

In this Note, we model an industrial system by a semi-Markov process where failure and repair phenomena are in mutual competition. A non-parametric estimation method for system component lifetime and repair time distributions and for associated hazard rate functions is proposed. The lifetime and repair time empirical distributions are reduced to two Kaplan–Meier estimators. A numerical example from an industrial system with three components and one repair man modeled by a birth and death process is provided to illustrate the previous results. To cite this article: A.-L. Afchain, C. R. Acad. Sci. Paris, Ser. I 339 (2004).