Fault tree truncation error bounds

Abstract

The solution of large fault trees can only performed if cut sets of a high order or low probability are neglected. This procedure is non-pessimistic since possible contributions to the top gate failure probability are ignored. Since the number of cut sets neglected is generally large, it is possible that their total contribution is significant compared to the total probability of those cut sets included in the evaluation of the top gate failure probability. In this paper a practical method for the estimation of upper bounds on the total failure probability of cuts sets of a given order is presented. This allows bounds on the contribution of all the cut sets neglected through cut-off procedures in fault tree solutions to be calculated, and so validate the top event failure probability. The method given here is much superior to that suggested by Modarres and Dezfuli in that it produces much lower and hence more useful bounds. The method of Modarres and Dezfuli can be refined, but for realistic fault tree examples the method given here always gives the least pessimistic and most practical bounds.