A two-dimensional software reliability growth model incorporating testing effort and coverage

Software reliability is a critical measure of software quality, particularly as software systems grow in complexity and scale. Traditional one-dimensional Software Reliability Growth Models (SRGMs), which primarily consider testing time as the influencing factor, often fail to capture the combined effect of multiple testing attributes on fault detection. This article proposes a two-dimensional SRGM that incorporates both testing effort and testing coverage to more accurately represent the software fault detection process. Two widely used Testing Effort Functions (TEFs)—Sigmoid and Weibull—are utilised, along with three distinct coverage functions—Exponential, Logistic, and Delayed S-shaped—to form six different model variants. These models are evaluated using a NASA dataset containing fault detection and multiple coverage metrics. Goodness-of-fit and predictive accuracy are assessed using statistical measures including R2, MSE, AIC, BIC, and Pham’s Criterion (PC). The results demonstrate that incorporating both testing coverage and effort significantly improves reliability estimation compared to conventional models. Among the proposed models, the Delayed S-shaped–Sigmoid model exhibited superior overall performance across most metrics. The findings highlight the importance of jointly modelling coverage and effort for improved software reliability prediction and resource allocation in practical testing environments.