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<p>In the contemporary landscape, software plays a crucial role in societal transformation and fostering innovation and driving technological transformation across social, economic and industrial sectors. This heightened reliance emphasises the need to study software reliability and develop models to predict it effectively. Given the competitive market and demand for high-quality software, firms continue to update their core product by releasing upgrades to address bugs, add new features, and enhance performance. To estimate software reliability and number of detected faults, many Software Reliability Growth Models (SRGMs) have been developed within the framework of probability theory, utilizing failure datasets collected during the testing. However, some epistemic uncertainties present in software failures cannot be adequately explained by probability theory, which arises from incomplete understanding and insufficient knowledge of software. Therefore, to address epistemic uncertainty associated with multiple versions, we propose a generalized novel Multi-Release Software Belief Reliability Growth Model (MRSBRGM). The developed model adopts an approach based on uncertain theory and belief reliability using uncertain differential equations, incorporating the epistemic uncertainties of software development across different releases. The methodology for estimating unknown parameters is derived using the least squares method. A Python code is created to estimate the parameter that quantifies the level of uncertainty in the model. Software reliability is examined under various reliability metrics, including belief reliable time, failure time between failures, and belief reliability for the proposed model. Numerical illustration is provided to demonstrate the accuracy of MRSBRGM. This model has been validated with two real datasets, specifically Gnome2 and Firefox, consisting of three releases. A comparative study has been conducted between the existing SRGM and the proposed model, and results show that our model performs well.</p>

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Multi-release software belief reliability growth model based on uncertain differential equation

  • 期刊论文

  • 发表日期：

    2025年12月17日

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  • Neelam Sharma,
  • Vijay Kumar,
  • Sunil Kumar Khatri

摘要

In the contemporary landscape, software plays a crucial role in societal transformation and fostering innovation and driving technological transformation across social, economic and industrial sectors. This heightened reliance emphasises the need to study software reliability and develop models to predict it effectively. Given the competitive market and demand for high-quality software, firms continue to update their core product by releasing upgrades to address bugs, add new features, and enhance performance. To estimate software reliability and number of detected faults, many Software Reliability Growth Models (SRGMs) have been developed within the framework of probability theory, utilizing failure datasets collected during the testing. However, some epistemic uncertainties present in software failures cannot be adequately explained by probability theory, which arises from incomplete understanding and insufficient knowledge of software. Therefore, to address epistemic uncertainty associated with multiple versions, we propose a generalized novel Multi-Release Software Belief Reliability Growth Model (MRSBRGM). The developed model adopts an approach based on uncertain theory and belief reliability using uncertain differential equations, incorporating the epistemic uncertainties of software development across different releases. The methodology for estimating unknown parameters is derived using the least squares method. A Python code is created to estimate the parameter that quantifies the level of uncertainty in the model. Software reliability is examined under various reliability metrics, including belief reliable time, failure time between failures, and belief reliability for the proposed model. Numerical illustration is provided to demonstrate the accuracy of MRSBRGM. This model has been validated with two real datasets, specifically Gnome2 and Firefox, consisting of three releases. A comparative study has been conducted between the existing SRGM and the proposed model, and results show that our model performs well.