S-shaped software reliability growth models derived from stochastic differential equations

Abstract

This paper presents a software reliability growth model based on Itô type Stochastic Differential Equations (SDE). As the size of a software system becomes larger, the number of faults remaining in the system during the testing phase can be considered to be a continuous stochastic process. In practice, if the per-fault detection rate is subject to certain random effects, we may consider the use of a SDE to describe the average behavior of the software fault detection process during the testing phase. As a result, we derive several software reliability measures by utilizing the mean value function which is the expected value of the SDE. We also derive the maximum likelihood estimators of the unknown parameters for the model. Futhermore, we compare our model with other software reliability growth models in terms of several reliability measures and goodness-of-fit for the same data set.