Error Propagation for Large Errors

An essential facet of a risk assessment is the correct evaluation of uncertainties inherent in the numerical results. If the calculation is based on an explicit algebraic expression, an analytical treatment of error propagation is possible, usually as an approximation valid for small errors. In many instances, however, the errors are large and uncertain. It is the purpose of this paper to demonstrate that despite large errors, an analytical treatment is possible in many instances. These cases can be identified by an analysis of the algebraic structure and a detailed examination of the errors in input parameters and mathematical models. From a general formula, explicit formulas for some simple algebraic structures that occur often in risk assessments are derived and applied to practical problems.