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<p>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 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 <i>O</i><sub><i>P</i></sub>(<i>n</i><sup>−3/7</sup>). In numerical experiment, the authors show that spline estimators under restriction demonstrate competitive performance compared to parametric and certain non-parametric models.</p>

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

  • 期刊论文

  • 发表日期：

    2026年2月5日

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  • Kangan Chen,
  • Jian Liu,
  • Qingpei Hu,
  • Min Xie

摘要

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 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 OP(n−3/7). In numerical experiment, the authors show that spline estimators under restriction demonstrate competitive performance compared to parametric and certain non-parametric models.