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Large-scale software exhibits periods of increased defect discovery when blocks of less thoroughly tested code are introduced into an existing codebase. For example, the mission systems schedule of software intensive government acquisition programs includes multiple overlapping software blocks associated with various capabilities. Software reliability researchers have proposed changepoint models to characterize periods of increased defect discovery. However, these models attempt to identify the location of these changepoints after testing has been performed, which is counter-intuitive because conscious decisions such as testing new functionality drive software changepoints. Existing changepoint models are therefore difficult to employ in a predictive manner. To overcome this limitation, this paper proposes a covariate software defect discovery model capable of explaining changepoints in terms of common software testing activities and metrics such as software size estimation, code coverage, and defect density. The proposed and past changepoint models are compared with respect to their predictive accuracy and computational efficiency. Our results indicate that the proposed approach is more computationally efficient and enables accurate prediction of the time needed to achieve a desired defect discovery intensity or mean time to failure despite the occurrence of changepoints during software testing.more » « lessFree, publicly-accessible full text available December 17, 2026
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ABSTRACT Traditional software reliability growth models (SRGM) characterize defect discovery with the Non‐Homogeneous Poisson Process (NHPP) as a function of testing time or effort. More recently, covariate NHPP SRGM models have substantially improved tracking and prediction of the defect discovery process by explicitly incorporating discrete multivariate time series on the amount of each underlying testing activity performed in successive intervals. Both classes of NHPP models with and without covariates are parametric in nature, imposing assumptions on the defect discovery process, and, while neural networks have been applied to SRGM models without covariates, no such studies have been applied in the context of covariate SRGM models. Therefore, this paper assesses the effectiveness of neural networks in predicting the software defect discovery process, incorporating covariates. Three types of neural networks are considered, including (i) recurrent neural networks (RNNs), (ii) long short‐term memory (LSTM), and (iii) gated recurrent unit (GRU), which are then compared with covariate models to validate tracking and predictive accuracy. Our results suggest that GRU achieved better overall goodness‐of‐fit, such as approximately 3.22 and 1.10 times smaller predictive mean square error, and 5.33 and 1.22 times smaller predictive ratio risk in DS1G and DS2G data sets, respectively, compared to covariate models when of the data is used for training. Moreover, to provide an objective comparison, three different proportions for training data splits were employed to illustrate the advancements between the top‐performing covariate NHPP model and the neural network, in which GRU illustrated a better performance over most of the scenarios. Thus, the neural network model with gated recurrent units may be a suitable alternative to track and predict the number of defects based on covariates associated with the software testing process.more » « lessFree, publicly-accessible full text available September 8, 2026
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Free, publicly-accessible full text available January 27, 2026
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Researchers have proposed several software reliability growth models, many of which possess complex parametric forms. In practice, software reliability growth models should exhibit a balance between predictive accuracy and other statistical measures of goodness of fit, yet past studies have not always performed such balanced assessment. This paper proposes a framework for software reliability growth models possessing a bathtub-shaped fault detection rate and derives stable and efficient expectation conditional maximization algorithms to enable the fitting of these models. The stages of the bathtub are interpreted in the context of the software testing process. The illustrations compare multiple bathtub-shaped and reduced model forms, including classical models with respect to predictive and information theoretic measures. The results indicate that software reliability growth models possessing a bathtub-shaped fault detection rate outperformed classical models on both types of measures. The proposed framework and models may therefore be a practical compromise between model complexity and predictive accuracy.more » « less
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