Reliability Analysis and Machine Learning Prediction for a Repairable Load-Sharing <italic>K</italic>-Out-of-<italic>N</italic> + <italic>W</italic>: G Power Supply System

Based on a power supply system, a repairable K-out-of-<inline-formula> <tex-math notation="LaTeX">$N+W$ </tex-math></inline-formula>: G system with c repairmen and warm spares is considered, where each repairman asynchronously takes multiple working vacations and vacation interruption policy. Total load of the system is shared equally by all the operating generators, the failure rate of each operating generator increases with the decreasing of the number of operating generators. Using Markov process and matrix-analytic method, steady-state probabilities and important performance indices are obtained. The mean time to first failure and reliability function are given by using the definition of PH-distribution. Numerical examples are given to illustrate the effect of system parameters on these reliability indices. In addition, machine learning (ML) methods including decision tree regression (DTR), random forest regression (RFR) and multilayer perceptron regression (MLPR) are used to predict the steady-state availability of the system, which shows that RFR is the optimal prediction model, and feature importances of system parameters are also provided.