Calculating Cumulative Operational Time Distributions of Repairable Computer Systems

We consider 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. We 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. We also show that other quantities of interest can be calculated as a byproduct of the method without any significant extra computational effort.