Uncertainty Propagation in Fault Tree Analyses Using Lognormal Distributions

This paper proposes a method for computing the uncertainty propagation in fault trees when the lognormal distribution is used as the probabilistic model for the basic-event failure rates. The method is based on approximating the NOT gate ``outputs'' by lognormal distributions and on transforming the OR gates into intersections. A computer code, PIAL, has been developed and is compared with other techniques for combining random variables. The results of some examples suggest that this new method is accurate enough. Its principal advantages are the short CPU time required (because it uses simple algorithms) and the conservation of the same uncertainty probabilistic model in the whole tree, ie, the lognormal distribution is used from basic events to the top event. So, two difficulties in uncertainty propagation are overcome: 1) methods giving good results (like Monte Carlo simulation and DPDs) require long computer times, and 2) no probability distribution propagates through logic operations.