Evaluating fault trees (AND and OR gates only) with repeated events

It is pointed out that a common practice in the evaluation of large fault trees is to truncate the computation by neglecting high-order or low-probability cutsets. A major disadvantage of most simple truncation methods, however, is that their accuracy is indeterminate because they do not establish rigorous bounds on the combined probability of the neglected cutsets. A truncated with residuals algorithm is presented. It uses probability-based truncation and determines a rigorous upper bound on each event-probability by propagating the effect of all the truncated cutsets in the form of numeric residuals. The method applies only to fault trees constructed entirely of AND and OR gates and allows unrestricted use of repeated events