Nanxiang Qiu
Graduate School of Advanced Science and Engineering, Hiroshima University, Hiroshima, Japan.

Tadashi Dohi
Graduate School of Advanced Science and Engineering, Hiroshima University, Hiroshima, Japan.

Jingchi Wu
Graduate School of Advanced Science and Engineering, Hiroshima University, Hiroshima, Japan.

Junjun Zheng
Graduate School of Advanced Science and Engineering, Hiroshima University, Hiroshima, Japan.

Hiroyuki Okamura
Graduate School of Advanced Science and Engineering, Hiroshima University, Hiroshima, Japan.

DOI https://doi.org/10.33889/IJMEMS.2026.11.5.076

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Abstract

Software reliability modeling is essential for assessing fault-detection behavior and predicting future software failures during the testing phase. Traditional nonhomogeneous Poisson process (NHPP)-based software reliability models (SRMs) are mathematically tractable, but they do not explicitly capture history-dependent fault-detection behavior. To address this limitation, this paper proposes a semi-parametric Hawkes process (HKP)-based SRM that combines an exponential time-varying base intensity with a shallow neural network (SNN) excitation kernel. The exponential base intensity represents the long-term decreasing trend of the background fault-detection rate, while the SNN excitation kernel flexibly learns the self-exciting effect induced by previous fault detections. To evaluate the expected cumulative number of detected faults, the mean value function is derived using an elementary approach for Hawkes processes and solved numerically. Experiments are conducted on eight real-world software fault-detection datasets. Our proposed semi-parametric SRM is compared with ten parametric HKP-based SRMs and representative NHPP-based SRMs using predictive mean squared error (PMSE). The results show that our proposed SRM achieves strong predictive performance, especially in early- and middle-stage prediction, and outperforms most competing SRMs in many settings. These findings indicate that the SNN excitation kernel provides a flexible and practically useful alternative for software reliability prediction.

Keywords- Software reliability model, Hawkes process, Self-excitation, Shallow neural network, Predictive performance.

Citation

Qiu, N., Dohi, T., Wu, J., Zheng, J., & Okamura, H. (2026). A Semi-Parametric Self-Exciting Software Reliability Model with Time-Varying Base Intensity and Shallow Neural Kernel. International Journal of Mathematical, Engineering and Management Sciences, 11(5), 1907-1928. https://doi.org/10.33889/IJMEMS.2026.11.5.076.