Fitting software reliability growth curves using nonparametric regression methods

A simple and effective method of assessing the reliability of a piece of software is to plot the cumulative number of failures observed during testing, N(x)N(x), against time xx. Since no software is ever completely free of errors, be it careless minor oversights or the results of serious design problems, it is therefore expected that with prolonged and systematic testing, N(x)N(x) will increase with xx. Since the 1970s, there have been many models, aptly named Software Reliability Growth Models (SRGMs) which have been proposed to fit software failure data to the curve m(x)=E(N(x))m(x)=E(N(x)). Unfortunately, due to the complexity of the software development processes, which include the possibility of imperfect debugging and introduction of new faults into the system, many of these SRGMs are very complex and standard estimation procedures such as Maximum Likelihood estimation (MLE) fails to estimate correctly, if at all, the parameters of these models. In this paper, we investigate the potential benefits of using Nonparametric Regression (NPR) methods to fit SRGMs. In addition, we will also develop methods based on Stein two-stage and modified two-stage sequential procedures to find a fixed-width confidence interval for the estimator of m(x)m(x). Finally, numerical examples based on real software failure data will be presented to illustrate the techniques developed and compare the results with some parametric SRGMs.