The impact of voltage sag on sensitive devices is related to the time when the sag occurs. However, the point-on-wave of a sag is uncertain. Therefore, this paper presents a novel approach to evaluate the voltage sag severity considering a random point-on-wave. First, the uncertainty of equipment malfunction is revealed. Second, under a given residual voltage, the relationship between the point-on-wave and the duration that the device can withstand is described with a fitting curve. Third, a voltage sag probabilistic index is proposed to describe the severity. The evaluation procedure is also presented. Finally, three types of releasers are tested and analyzed to determine the effectiveness of the proposed method. The evaluation method can help instruct electrical engineers establish more well-grounded sag mitigation proposals.