In the present paper, we aim at providing plug-in-type empirical estimators based on empirical processes to quantify the contribution of each operational or/and non-functioning state to the failures of a system described semi-Markov model. In particular we focus on an important reliability measure for random repairable systems, the rate of occurrence of failures and study different conditional versions in a discrete time and finite state space context. The aforementioned esti-mators of the conditional failure occurrence rates are caracterised by appealing asymptotic properties such as consistency and asymptotic normality. We further provide detailed analytical expressions for the covariance matrices of the random vectors describing the conditional failure occurrence rates. These results are illustrated on an academ-ical numerical example based on simulated data. We further present an application to a real dataset that models earthquake occurrences in a semi-Markov framework.