Often, during a layer of protection analysis (LOPA) or a quantitative risk analysis (QRA) study, historical information indicates no occurrences of a particular undesired event in the plant or system. The simple reply that the frequency or rate is zero because the event has never happened is sometimes heard by the analyst during review meetings. The analyst must then decide on an appropriate measure of the frequency of the undesired event. This article presents methods based on statistical tools for developing a measure of the frequency or failure rate of an event when the historical information includes no occurrences of the event. The article compares the various available statistical tools. Guidance is presented on methods to incorporate historical information of no failures into a LOPA or QRA study. Examples on the application of the recommended methods to deal with the problem are presented. (C) 2011 American Institute of Chemical Engineers Process Saf Prog 30: 204-211, 2011