A birth-process approach to Moranda's geometric software-reliability model

To alleviate some of the objections to the basic Jelinski Moranda (JM) model for software failures, Moranda proposed a geometric de-eutrophication model. This model assumes that the times between failures are statistically-independent exponential random variables with given failure rates. In this model the failure rates decrease geometrically with the detection of a fault. Using an intuitive approach, Musa, Iannino, Okumoto , see also Farr , derived expressions for the mean and the intensity functions of the process N (t) which counts the number of faults detected in the time interval O, t] for the Moranda geometric de-eutrophication model. N (t) is studied as a pure birth stochastic process; its probability generating function is derived, as well as its mean, intensity and reliability functions. The expressions for the mean and intensity functions derived by MIO are only approximations and can be quite different from the true functions for certain choices of the failure rates. The exact expressions for the mean function and the intensity function of N (t) are used to find the optimum release time of software based on a cost structure for Moranda's geometric de-eutrophication model.