(101d) What to Do When Nothing Has Happened?

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 analyst must decide on an appropriate measure of the frequency of the undesired event. 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. Previously, Freeman presented a summary of twelve statistical tools that have been proposed to handle this problem. This paper expands on the previous work and adds another statistical tool for developing a measure of the frequency or failure rate of an event when the historical information includes no occurrences of the event. Guidance is presented on methods to incorporate historical information of no failures into a LOPA or QRA study. Examples are presented using the recommended methods for the estimation of initiating event frequencies where historical information indicates that the initiating event has not happened.