Mathematical Modelling In Software Reliability

A mathematical model based on stochastic and statistics theories is useful to describe the software fault-removal phenomena or the software failure-occurrence phenomena and estimate the software reliability quantitatively. A mathematical tool which describes software reliability aspect is a software reliability growth model (SRGM). Discrete time models in software reliability are important and a little effort has been made in this direction. Their importance cannot be underestimated since the number of test cases is more appropriate measure of the fault removal/detection period than the CPU/calendar time used by continuous time model. These models generally provide a better fit than their continuous time counterparts. It is important to note that due to the complexity of software design, it is not expected that any single model can incorporate all factors which are thought to influence software reliability. In this paper, we show how beginning with very simple assumptions, non-homogenous Poisson process (NHPP) type of discrete time SRGMs, are gradually made more realistic with the incorporation of imperfect debugging, involvement of a learning-process in debugging and introduction of new faults. The applicability of the resultant generalized model is demonstrated through several actual software reliability data sets obtained from different software development projects. The proposed generalized model is also checked against different components of the model, including existing one, thus highlighting its applicability.