Local probabilistic sensitivity measures for comparing FORM and Monte Carlo calculations illustrated with dike ring reliability calculations

We define local probabilistic sensitivity measures as proportional to parti al derivative E(X-i\Z = z)/partial derivative z, where Z is a function of r andom variables X1, ..., X-n. These measures are local in that they depend only on the neighborhood of Z = z, but unlike other Local sensitivity measu res, the local probabilistic sensitivity of X-i does not depend on values o f other input variables. For the independent linear normal model, or indeed for any model for which X-i has linear regression on Z, the above measure equals sigma x(i)rho(Z, X-i)/sigma(Z). When linear regression does not hold , the new sensitivity measures can be compared with the correlation coeffic ients to indicate degree of departure from linearity. We say that Z is probabilistically dissonant in X-i at Z = z if is increasi ng (decreasing) in X-i at z, but probabilistically decreasing (increasing) at z. Probabilistic dissonance is rather common ill complicated models. The new measures are able to pick up this probabilistic dissonance. These notions are illustrated with data from an ongoing uncertainty analysi s of dike ring reliability. (C) 1999 Elsevier Science B.V.