Quantitative Calculations Using the Fault Tree

The fault tree can be used to perform quantitative calculations to determine the probability of the top event. This is accomplished in two ways. 

The other procedure is to use tl e minimal cut sets. This procedure approaches the exact result only if the probabilities of all the events are small. In general, this result provides a number that is larger than the actual probability. This approach assumes that the probability cross-product terms shown in Equation 11-10 are negligible. 

The minimal cut sets represent the various failure modes. For Example 11-6 events 1,3 or 2,3 or 1,4 or 2,4 could cause the top event. To estimate the overall failure probability, the probabilities from the cut sets are added together. For this case 

This compares to the exact result of 0.0702 obtained using the actual fault tree. The cut sets are related to each other by the OR function. For Example 11-6 all the cut set probabilities were added. This is an approximate result, as shown by Equation 11-10, because the cross-product terms were neglected. For small probabilities the cross-product terms are negligible and the addition will approach the true result. 

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