A simple approach to reliability, risk, and uncertainty analysis of hydrologic, hydraulic, and environmental engineering systems

Scope and method of study. The purpose of this study was to develop a simple and accurate procedure for uncertainty, risk, and reliability analysis of hydrologic, hydraulic, and environmental engineering systems. For uncertainty analysis, the objective was to develop a correction procedure to correct the first order approximation estimates for the model nonlinearity, parameter uncertainty, and parameter distribution types. For reliability and risk analysis, the objective was to develop a simple and generalized technique to determine higher-order moments of a model output as a function of the means, the coefficient of variations, and the distribution types for input random variables.; Findings and conclusions. The exactness of the first order approximation estimates depends up on three factors: parameter coefficient of variation, parameter distribution type, and degree of nonlinearity in the functional relationship. Analytical as well as graphical relationships for relative error are developed for generic power and exponential functions. These relationships can be used as a guide to judge the suitability of the first order approximation for a specified acceptable error of estimation. Further, these relationships can be used to correct the first order approximation estimates of means and variances of model components for parameter uncertainty, parameter distribution type, and model non-linearity to their corrected values. Using these corrected values of means and variances for model components, one can determine the exact values of the mean and variance of a model. Knowledge of higher-order moments helps in identifying the appropriate distribution for the model output. A simple approach of developing generic expectation functions is described. Analytical expressions of generic expectation functions for generalized power and exponential functions are derived using several commonly used input parameter distributions. These expectation functions can be used to determine exact estimates of any order of model output moments.