Power systems with photovoltaic (PV) arrays combined with battery backup storage are becoming increasingly used because of their capability of working in power island mode, especially during grid outages. The problem is to decide the optimal battery sizes for PV + battery systems with given solar array sizes, from both power supply reliability and economical perspectives. An optimization method based on the simulation of system operation during grid interruption is developed to investigate the effects of battery size on system output reliability level of meeting load demand with minimum cost. Case studies are conducted for validation according to actual solar irradiation data, load profiles and realistic power interruption statistics. Sensitivity analysis is also performed to explore how system total cost affects islanding capability of a PV + battery system to supply energy to facilities. The finding shows that the decline of battery price not only reduces the lowest system total cost but also improves islanded system generation reliability. The proposed methodology for optimizing battery capacity added to PV array systems can make them grid-outage resilient and economically viable, which can be utilized as a decision-making tool for future PV + battery system expansion.