Wavelet-Based Approach for Estimating Software Reliability

Recently, wavelet methods have been frequently used for not only multimedia information processing but also time series analysis with high speed and accuracy requirements. In this paper we apply the wavelet-based techniques to estimate software intensity functions in non-homogeneous Poisson process based software reliability models. There are two advantages for use of the wavelet-based estimation; (i) it is a non-parametric estimation without specifying a parametric form of the intensity function under any software debugging scenario, (ii) the computational overhead arising in statistical estimation is rather small. Especially, we apply two kinds of data transforms, called Anscombe transform and Fisz transform, and four kinds of thresholding schemes for empirical wavelet coefficients, to non-parametric estimation of software intensity functions. In numerical validation test with real software fault data, we show that our wavelet-based estimation method can provide higher goodness-of-fit performances than the conventional maximum likelihood estimation and the least squares estimation in some cases, in spite of its non-parametric nature.