Development and evaluation of an uncertainty importance measure in fault tree analysis

In a fault tree analysis, an uncertainty importance measure is used to identify those basic events that significantly contribute to the uncertainty of the top-event probability. This paper defines an uncertainty importance measure of a basic event or of a group of basic events, and develops a two-stage procedure for experimentally evaluating the measure under the assumption that the probability of each basic event follows a lognormal distribution. The proposed method utilizes the Taguchi tolerance design technique with modifications. Then, the so-called contribution ratios which evaluate the main and/or interaction effects of the uncertainties of log-transformed basic-event probabilities on the uncertainty of the log-transformed top-event probability are calculated. The contribution ratios are used to estimate the defined uncertainty importance measure of a basic event or of a group of basic events. The proposed method consists of two stages for computational efficiency. In the first stage, the basic events with negligible effects on the uncertainty of the log-transformed top-event probability are screened out, and more detailed analyses are conducted in the second stage with a substantially smaller number of basic events. In addition, this paper presents an analysis method to quantify the percentage reduction in the uncertainty of the log-transformed top-event probability when the uncertainty of each basic-event probability is reduced.