The detection of losses of special nuclear materials has been the subject of much research in recent years. The standard industry practice using ID/LEID will detect large magnitude losses. Time series techniques such as the Kalman Filter or CUSUM methods will detect small magnitude losses if they occur regularly over a sustained period of time. To date no technique has been proposed which adequately addresses the problem of detecting a small magnitude loss occurring in a single period. This paper proposes a method for detecting a small magnitude loss. The approach makes use of the influence function of Hempel. The influence function measures the effect of a single inventory difference on a group of statistics. An inventory difference for a period in which a loss occurs can be expected to produce an abnormality in the calculated statistics. This abnormality is measurable by the influence function. It is shown that a one period loss smaller in magnitude than the LEID can be detected using this approach