In this paper, we derive an software mixed debugging model based on a Markov process, assuming that the length of time to perform the debugging is random and its distribution may depend on the fault type causing the failure. We assume that the debugging process starts as soon as a software failure occurs, and either a perfect debugging or an imperfect debugging is performed upon each fault type. One type is caused by a fault that is easily corrected and in this case, the perfect debugging process is performed. An Imperfect debugging process is performed to fix the failure caused by a fault that is difficult to correct. Distribution of the first passage time and working probability of the software system are obtained; in addition, an availability function of a software system which is the probability that the software is in working at a given time, is derived. Numerical examples are provided for illustrative purposes.