A comparative study: top event unavailability by point estimates and uncertainty propagation

The results of five cases studied are presented to identify how close the cumulative value represented by the point estimate is to the corresponding statistics of the top event distribution. The computer code FTA-J is used for quantification of the fault trees studied, top event unavailabilities, moments and cumulative probability distributions inclusive. The FTA-J demonstrates its usefulness for large trees. In all cases, the point estimate unavailability of the top event based on the median values of the basic events, which has been widely and commonly used in risk assessment for the sake of its simplicity, are lower than its median unavailability by uncertainty propagation. The top event unavailability thus obtained can represent much lower values: i.e. the system would appear much better than it actually is. The point estimate based on the mean values, however, is shown the same as that obtained by uncertainty propagation numerically and analytically. The mean of the top event can be well approximated by forming the product of the means of the components in each cut set, then summing these products. The point estimate can not represent all of the probability distribution characteristics of the top event, so that the estimation of probability intervals for the top event unavailability should be made either by a Monte Carlo simulation or other analytical method. When it is forced to calculate the top event unavailability only by the point estimate, it is the mean value of the component failure data that should be used for its quantification. (author)