Point availability and expected interval availability are dependability measures respectively defined by the probability that a system is in operation at a given instant and by the mean percentage of time during which a system is in operation over a finite observation period. We consider a repairable computer system and we assume as usual that the system is modeled by a finite Markov process. We propose in this paper a new algorithm to compute these two availability measures. This algorithm is based on the classical uniformization technique in which a test to detect the stationary behavior of the system is used to stop the computation if the stationarity is reached. In that case, the algorithm gives not only the transient availability measures but also the steady state availability, with significant computational savings especially when the time at which measures are needed is large. In the case where the stationarity is not reached, the algorithm provides the transient availability measures and bounds for the steady state availability. It is also shown how the new algorithm can be extended to the computation of performability measures.