A Second-Order Moments Method for Uncertainty Analysis

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Abstract
The system moments approach is extended to combine random variables for large systems. A computer code, COSMOS, has been developed to propagate uncertainties for systems which contain up to 100 components. Extension of the method to very large systems is possible by modular evaluation. An example illustrates the method for evaluating the distribution of the top event unavailability for a fault tree. Advantages of the method include small required execution times and the avoidance of random number generation. Application of the method to Boolean sum-of-products representations of fault trees provides results which are consistent with the Monte Carlo method since, for this special case, higher order derivatives are zero. Serious limitations to the method include: unquantifiable accuracy for functions whose higher derivatives are non-zero (as is often the case), inability to model s-dependent failures as the moments equations assume s-independence, and difficulty in improving the accuracy of the method (compared with Monte Carlo evaluation which may be arbitrarily improved).