An Improved Computation Procedure for Risk Analysis Problems With Unusual Probability Functions

Abstract

Abstract A computational method called Latin Hypercube Sampling (LHS) has been developed. LHS is superior to Monte Carlo simulation for risk analysis problems which involve discrete probability distributions containing events having very small probabilities but drastically large effects on the final solution. The LHS method is applied with evenly spaced probability intervals for a random variable. Each interval is then sampled without replacement, thus avoiding clustering of values. Monte Carlo simulation has the disadvantage that random samples may become clustered in an apparent biased fashion until a large number have been selected. LHS, in effect, forces samples to correspond more closely to a given probability distribution earlier in the selection process. Examples are shown comparing the number of computations with Monte Carlo simulation, which has a very slow convergence in the example cases, to a relatively accurate and rapid computation by the LHS method. We were able to show that the LHS method can be used to advantage in problems having smooth probability functions as well as abnormal probability functions.