The fault reduction factor (FRF) is a significant parameter for controlling the software reliability growth. It is the ratio of net fault correction to the number of failures encountered. In literature, many factors affect the behaviour of FRF, namely fault dependency, debugging time-lag, human learning behaviour and imperfect debugging. Besides this, several distributions, for example, inflection S-shaped, Weibull and Exponentiated-Weibull, are used as FRF. However, these standard distributions are not flexible to describe the observed behaviour of FRFs. This paper proposes three different software reliability growth models (SRGMs), which incorporate a three-parameter generalized inflection S-shaped (GISS) distribution as FRF. To model realistic SRGMs, time lags between fault detection and fault correction processes are also incorporated. This study proposed two models for the single release, whereas the third model is designed for multi-release software. Moreover, the first model is in perfect debugging, while the rest of the two are in an imperfect debugging environment. The extensive experiments are conducted for the proposed models with six single release and one multi-release data-sets. The choice of GISS distribution as an FRF improves the software reliability evaluation in comparison with the existing systems in the literature. Finally, the development cost and optimal release time are calculated in a perfect debugging environment.
