An Analytic Method for Uncertainty Analysis of Nonlinear Output Functions, with Applications to Fault-Tree Analysis

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Abstract
An analytic method for uncertainty analysis of the output of a complex model is described. It is assumed that model inputs are s-independent random variables and that model output is given as an analytic though possibly nonlinear function of the inputs. Using conditional s-expectations as a tool, a theoretical basis is developed for a method of partitioning the variance of the output among contributing causes. Such a partitioning helps the system analyst to identify the most important contributors to output uncertainty and, hence, to find effective ways of reducing that uncertainty. The method is illustrated by application to the uncertainty analysis of fault trees. There is no reason, in principle, why the method should not be applied to large computer codes where output cannot be represented as an analytic function of input. However, the evaluation of the required conditional s-expectations in such cases would be likely to involve considerable computation. It would be very desirable to extend the method to handle the case of s-correlated input variables. However, the partitioning of output variance in the presence of s-dependent inputs is difficult. The difficulties involved have not yet been resolved except in simple cases of s-dependence which can be reduced to the s-independent case by transformations of variables or other devices.

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