Uncertainty analysis using corrected first-order approximation method

Application of uncertainty and reliability analysis is an essential part of many problems related to modeling and decision making in the area of envir onmental and water resources engineering. Computational efficiency, underst andability, and easier application have made the first-order approximation (FOA) method a favored tool for uncertainty analysis. In many instances, si tuations may arise where the accuracy of FOA estimates becomes questionable . Often the FOA application is considered acceptable if the coefficient of variation of the uncertain parameter(s) is <0.2, but this criterion is not correct in all the situations. Analytical as well as graphical relations fo r relative error are developed and presented for a generic power function t hat can be used as a guide for judging the suitability of the FOA for a spe cified acceptable error of estimation. Further, these analytical and graphi cal relations enable FOA estimates for means and variances of model compone nts to be corrected to their true values. Using these corrected values of m eans and variances for model components, one can determine the exact values of the mean and variance of an output random variable. This technique is a pplicable when an output variable is a function of several independent rand om variables in multiplicative, additive, or in combined (multiplicative an d additive) forms. Two examples are given to demonstrate the application of the technique.