We consider a system modeled by a semi-Markov process where we include geometric renewal process for sojourn times. Pérez-Ocón and Torres-Castro first study this system [1]. In our work here we consider an extended state space for up and down times separately. This allows us to use the standard theory for semi-Markov processes in order to obtain all reliability related measurements as reliability, availability (point and steady-state), mean times and rate of mortality of the system with general initial law. We proceed with a convolution algebra, which allows us to obtain final closed form formulas for the above measurements. Moreover, we present numerical examples.