Software reliability analysis via geometric de-eutrophication models with group data

In this paper, we focus on a pure birth process to describe software fault counts, called the geometric de-eutrophication software reliability model (SRM), and provide some useful results to handle the software fault count group data. Two types of SRMs are considered; Moranda SRM (1975) and Gaudoin-Soler SRM (1992), where the former is a modification of the well-known Jelinski-Moranda SRM (1972) having a software fault detection rate with geometrically decreasing reduction, the latter is an extension of Moranda SRM having another software fault detection rate with exponential decay. First, we note that these two SRMs are essentially identical. For the software fault-detection time data, the above geometric de-eutrophication SRM has been used to quantify the software reliability. Unfortunately, it is emphasized that the group data analysis with the geometric de-eutrophication SRM has not been done yet in the literature. We formulate the maximum likelihood estimation of the geometric de-eutrophication SRM and perform the software reliability analysis with the fault count group data, which can be observed in the software industry. Throughout numerical examples with the real software fault count group data, we investigate the goodness-of-fit and predictive performances for the geometric de-eutrophication SRM and compare it with the seminal Jelinski-Moranda SRM.