In this work we investigate the influence of various memory chips supply voltage on their sensitivity to the radiation environment. The main physical mechanisms responsible for radiation-induced degradation at nominal, increased, and decreased supply voltage values are discussed. It is demonstrated that, depending on supply voltage value during irradiation and subsequent testing, device's tolerance to data corruption effects in memory circuits, single event latch-up (SEL) and hard errors induced by ionizing radiation can vary significantly. We also give some recommendations to perform radiation tests.