Software Reliability Prediction Using Chaotic Convolution Neural Network and Chi-square-based Grey Wolf Algorithm

doi:10.1007/s10836-026-06259-w

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Software Reliability Prediction Using Chaotic Convolution Neural Network and Chi-square-based Grey Wolf Algorithm

2026-09-23

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Neha Yadav *

Mukul Aggarwal

Kamal Kant Sharma

DOI：10.1007/s10836-026-06259-w

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Abstract

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A software reliability prediction is a vital process used to assess software quality and the reliability of the software system during testing and deployment. The characteristics of software failure data, which are non-linear, dynamic, and uncertain, however, make accurate estimation of reliability difficult. However, traditional Software Reliability Growth Models (SRGMs) and machine learning (ML) models may find it difficult to model complex failure behaviour and have unstable prediction performance when trained with limited testing data. To solve these problems, a hybrid software reliability prediction model, Chaotic Convolutional Neural Network with Chi-square-based Grey Wolf Optimization algorithm (CCNN-CGWO), is proposed in this paper. According to the proposed structure, the software failure data are first transformed by the Logistic chaotic map to improve the nonlinear feature representation. The data are then transformed and processed with Chaotic Convolutional Neural Network (CCNN) to obtain the deep failure patterns and estimate the parameters of reliability. Later, the Chi-square-based Grey Wolf Optimization (CGWO) algorithm is used to optimize the estimated parameters to minimize the statistical differences between the predicted and observed failure behaviour. Moreover, a testing effort function is added to realistically model the actual dynamics of software testing and enhance prediction accuracy. The proposed framework is tested using data on computer software failure of DS1 and DS2 Tandem computer software and is compared with Goel–Okumoto, TEF-based SRGM models, GWO-SRGM and CGWO-SRGM. The experimental results indicate that the proposed CCNN-CGWO model can obtain a low value of prediction error with MSE values of 0.021 and 0.020, RE values of 0.022 and 0.020 for DS1 and DS2, respectively, and R2 values of 0.99 and Chi-square fitness values of 2.5 and 2.3 for DS1 and DS2, respectively. The results show that the proposed CCNN-CGWO model can predict software reliability more accurately and robustly than the current models.

Keywords:

Software reliability growth model

Chaotic convolutional neural network

Testing effort function

Grey Wolf Optimisation

Mean squared error