The generalized software reliability model on the basis of non-stationary Markovian service system is proposed. Approximation by Coxian distribution allows investigating software reliability growth for any kinds of distribution (for example, Weibull, Gamma) of time between the moments of program errors detection and fixing. The model enables to forecast important software reliability characteristics, such as number of corrected errors, number of errors to be fixed, required debugging time, etc. The diagram of transitions between states of the generalized model and differential equations system are presented. The example of calculation with use of the offered model is considered, research of influence of Coxian distributions variation coefficients of duration of intervals between the error detection moments and error correction time distributions on values of look-ahead characteristics is executed.