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.

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Software reliability is one of the standard critical inherent characteristics of software systems. The testing coverage function (TCF) is a significant parameter for identifying the completeness and effectiveness of software testing. It is defined as the proportion of the code that has been tested up to time t. To capture the dynamic behavior of the number of faults detected over a period of time, several distributions, namely S‐shaped, inflection S‐shaped, logistic, log‐logistic, Weibull, Rayleigh, Erlang, and logarithmic exponentiated, have been used as TCF in literature. However, these distributions are not sufficient to describe TCF's practical behavior due to complexity and vagueness in the collected data. This study proposes two software reliability growth models (SRGMs), which incorporate the generalized inflection S‐shaped (GISS) distribution as TCF. The models have been developed in perfect and imperfect debugging environments while considering fault removal efficiency, error generation, and uncertainty in the operating environment. To analyze the effectiveness, the proposed models are then tested with six failure data sets. The choice of GISS distribution as a TCF improves the software reliability estimation in comparison with the existing models in the literature. Finally, single and multiple parameters sensitivity analysis also has been done and based on it, the critical parameters have been detected. The proposed models may be helpful for the system analyst to predict various parameters about some software systems.

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