The rate of occurrence of failures for semi-Markov processes and estimation

This paper investigates the rate of occurrence of failures (ROCOF) of finite state semi-Markov systems. Firstly, a formula for evaluating the ROCOF for semi-Markov systems is derived. As a consequence of this result, we derive the ROCOF of Markov systems as well as the ROCOF of the alternating renewal processes and we give their asymptotic values. From the semi-Markov ROCOF formula, we propose a statistical estimator of this function. Finally, the uniform strong consistency and the asymptotic normality of this estimator are obtained.