Repairable computer systems are considered, the availability behavior of which can be modeled as a homogeneous Markov process. The randomization method is used to calculate various measures over a finite observation period related to availability modeling of these systems. These measures include the distribution of the number of events of a certain type, the distribution of the length of time in a set of states, and the probability of a near-coincident fault. The method is then extended to calculate performability distributions. The method relies on coloring subintervals of the finite observation period based on the particular application, and then calculating the measure of interest using these colored intervals. © 1989, ACM. All rights reserved.