Statistical Inference for Software Reliability Constrained by the Shape of the Mean Value Function

While parametric Software Reliability Growth Models (SRGMs) serve as a cornerstone in software reliability assessment, their reliance on known fault-detection time distributions often presents a significant limitation in practical software testing. In this study, the authors  develop a novel shape-restricted spline estimator for quantifying software reliability. Compared with parametric SRGMs, the proposed estimator not only shares a key characteristic with parametric SRGMs, but also obviates the need for specifying fault-detection time distributions. More importantly, it effectively utilizes the critical shape information of the mean value function (MVF) of the fault-detection process, a detail seldom considered in prior work. Moreover, the authors  investigate the predictive performance of the proposed methods by employing the so-called one-step look-ahead prediction method. Furthermore, the authors  show that under certain conditions, the shape-restricted spline estimator will attain the point-wise convergence rate. In a numerical experiment, the authors show that spline estimators under restriction demonstrate competitive performance compared to parametric and certain non-parametric models.