Wavelet Shrinkage Estimation for Non-Homogeneous Poisson Process Based Software Reliability Models

We develop a novel estimation approach for quantitative software reliability by means of wavelet-based technique, where the underlying software reliability model is described by a non-homogeneous Poisson process. Our approach involves some advantages over the commonly used techniques such as maximum likelihood estimation: 1) the wavelet shrinkage estimation enables us to carry out the time-series analysis with high speed and accuracy requirements; and 2) The wavelet shrinkage estimation is classified into a non-parametric estimation without specifying a parametric form of the software intensity function. We consider data-transform-based wavelet shrinkage estimation with four kinds of thresholding schemes for empirical wavelet coefficients to estimate the software intensity function. In numerical experiments with real software-fault count data, we show that our wavelet-based estimation methods can provide better goodness-of-fit performance than not only the conventional maximum likelihood estimation and least squares estimation but also the local likelihood estimation method, in many cases, in spite of their non-parametric nature. Furthermore, we investigate the predictive performance of the proposed methods by employing the so-called one-stage look-ahead prediction method, and estimate some predictive measures such as software reliability.