Abstract
Mathematical studies about the likelihood of failures of software systems have been advanced by various researchers. These studies have modeled the behavior of software systems by using failure times and time between failures in the past. The Goel-Okumoto software reliability model is amongst the many software reliability models proposed to model the failure behavior of software systems. To be able to use the model in software reliability assessment, it is important to estimate its parameters α and β and the intensity function λ(t). In this paper, classical parametric regression methods have been utilized in the estimation of the parameters α and β, the intensity function and the mean time between failures of the Goel-Okumoto software reliability model. The parameters α and β and the mean time between failures (MTBF) of the Goel-Okumoto software model have been estimated using the maximum likelihood estimation (MLE) method, regression approach applied to the model and simple linear regression model without assuming the Goel-Okumoto model. When these three estimation methods were validated using root mean squared error (RMSE) and mean absolute value difference (MAVD), which are the common error measurement criteria, regression approach applied to the Goel-Okumoto model outperformed MLE and simple linear regression estimation methods.
Highlights
Various software reliability growth models have been proposed in the last three decades
The results obtained from the maximum likelihood estimation (MLE) method, regression method and simple linear regression method are respectively given in subsections 3.1.1, 3.1.2 and 3.1.3
Using Maximum Likelihood Estimation Method From Equations (10) and (11) and the data in Table 1, the MLE of the parameters α and β of the Goel-Okumoto software reliability model with intensity function given in Equation (1) are αmle = 31.698171 and βmle = 0.003962
Summary
Various software reliability growth models have been proposed in the last three decades. Amongst the many software reliability growth models is the Goel – Okumoto software reliability model, a NonHomogeneous Poisson process (NHPP) with intensity function λ (t ) = αβ e−βt (1). The software reliability model with intensity function given in Equation (1) was proposed by [1] in 1979 the name Goel-Okumoto (1979) software reliability model. The reliability and the behavior of the software systems are studied by estimating the parameters of the software growth models. Various parameter estimation criteria have been advanced by different researchers in the past. For instance, [2], [3] and [4] have considered estimation of the parameters of Goel-Okumoto (1979) software reliability model whose intensity function is given in Equation (1) using MLE criteria. Literature from various research, for instance, [5, 6] and [7] have indicated that the Goel-Okumoto software reliability model is a good model to represent TBF of software systems
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