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Abstract Modeling and evaluation of a system reliability is a key issue in shock model analysis. In cumulative shock model, a system fails when the total damages caused by shocks exceeds the system failure threshold level. The reliability of a system with random failure threshold level under cumulative shocks is investigated in this work, considering the general dependency between inter‐arrival times of shocks and their damages magnitudes. Clustering, as one of the unsupervised machine learning methods, is utilized here by applying a genetic algorithm (GA) and particle swarm optimization algorithm (PSO) for its implementation. Phase‐type (PH) distributions and their properties are also applied for finding a system failure distribution functions, determining the convolutions, evaluating the integrals, and ultimately modeling the system reliability. An illustrative example is provided to demonstrate the implementation and effectiveness of the proposed modeling procedure and the suggested approach for computing the system reliability and remaining useful lifetime (RUL). Also, an example case study of X‐ray machine in healthcare industry is provided to demonstrate the application of the proposed model. Applying other machine learning methods for patterns recognition is an area for future research.
Shamstabar et al. (Thu,) studied this question.