The power system of an all-electric ship (AES) establishes an independent microgrid using the distributed energy resources, energy storage devices, and power electronic converters. As a hybrid energy system (HES), the power system of an AES works as a unified system where each part can affect the reliability of the other parts. The systemic reliability centered maintenance (SRCM), which efficiently enhances the reliability and safety of the AES by identifying optimal maintenance tasks of the AES, is considered in this article to apply to the entire system. In order to calculate the reliability and optimal maintenance schedule, the Markov process and Enhanced JAYA (EJAYA) are utilized. A layer of protection analysis (LOPA), which is a risk management technique, is adopted to assess the safety of the system. A hybrid molten carbonate fuel cell, photovoltaic (PV), and lithium-ion battery are considered as energy sources of the AES. Based on two common standards, DNVGL-ST-0033 and DNVGL-ST-0373, the suggested maintenance planning method can be used in industrial applications. Eventually, in order to validate the proposed method, a model-in-the-loop real-time simulation using dSPACE is carried out. The obtained results show the applicability and efficiency of the proposed method for improving reliability and safety.