Consideration is given to repairable computer systems, those for which repair can be performed to put the system back in operation. The behavior of the system is assumed to be modeled as a homogeneous Markov process. The authors calculate numerically the distribution of cumulative operational time, which is the distribution of the total time during which the system was in operation over a finite observation period. The method is based on the randomization technique. The main advantages include the ability to specify error tolerances in advance, numerical stability, and simplicity of implementation. It is also shown that other quantities of interest can be calculated as a by-product of the method without any significant extra computational effort.