Abstract
Advances in machine learning (ML) have led to applications in safety-critical domains, including security, defense, and healthcare. These ML models are confronted with dynamically changing and actively hostile conditions characteristic of real-world applications, requiring systems incorporating ML to be reliable and resilient. Many studies propose techniques to improve the robustness of ML algorithms. However, fewer consider quantitative techniques to assess changes in the reliability and resilience of these systems over time. To address this gap, this study demonstrates how to collect relevant data during the training and testing of ML suitable for the application of software reliability, with and without covariates, and resilience models and the subsequent interpretation of these analyses. The proposed approach promotes quantitative risk assessment of ML technologies, providing the ability to track and predict degradation and improvement in the ML model performance and assisting ML and system engineers with an objective approach to compare the relative effectiveness of alternative training and testing methods. The approach is illustrated in the context of an image recognition model, which is subjected to two generative adversarial attacks and then iteratively retrained to improve the system's performance. Our results indicate that software reliability models incorporating covariates characterized the misclassification discovery process more accurately than models without covariates. Moreover, the resilience model based on multiple linear regression incorporating interactions between covariates tracks and predicts degradation and recovery of performance best. Thus, software reliability and resilience models offer rigorous quantitative assurance methods for ML-enabled systems and processes.