Functions of Random Variables: Error Propagation

Abstract

This chapter contains the core of engineering risk analysis, the central theme about which the rest of the material pivots. In Civil Engineering almost all designs involve some calculation using an equation that is based on the physics of the problem, empirical data of the phenomenon, or a combination of the two (often called semi-empirical equations). The parameters in these equations are routinely treated as deterministic and it is common to use mean or median values for calculation purposes. But if we treat these parameters as random variables and propagate the uncertainty through the equations we get a much better understanding of the most likely answer, as well as an understanding of how much confidence we should have in that most likely answer. Through this process of error propagation we fully characterize the problem by accounting for the uncertainty of the input variables and their mathematical interrelationship as described in the engineering equation. This sets the stage for determining how accurate the answer is, how much confidence we can have in the mean or median, and how best to proceed to ensure a reliable engineering design.