Mathematical representation of uncertainty

Abstract

As widely done in the risk assessment community, a distinction is made between aleatory (random) and epistemic (subjective) uncertainty in the modeling and simulation process. The nature of epistemic uncertainty is discussed, including (1) occurrence in parameters contained in mathematical models of a system and its environment, (2) limited knowledge or understanding of a physical process or interactions of processes in a system, and (3) limited knowledge for the estimation of the likelihood of event scenarios of a system. To clarify the options available for representation of epistemic uncertainty, an overview is presented of a hierarchy of theories of uncertainty. Modern theories of uncertainty can represent much weaker statements of knowledge and more diverse types of uncertainty than traditional probability theory. A promising new theory, evidence (Dempster-Shafer) theory, is discussed and applied to a simple system given by an algebraic equation with two uncertain parameters. Multiple sources of information are provided for each parameter, but each source only provides an interval value for each parameter. The uncertainty in the system response is estimated using probability theory and evidence theory. The resultant solutions are compared with regard to their assessment of the likelihood that the system response exceeds a specified failure level. In this example, a traditional application of probability theory results in a significantly lower estimate of risk of failure as compared to evidence theory. Strengths and weaknesses of evidence theory are discussed, and several important open issues are identified that must be addressed before evidence theory can be used successfully in engineering applications. * Distinguished Member Technical Staff, Associate Fellow t Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the U. S. Department of Energy under contract No. DEAC04-94AL85000. This paper is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Kari Sentz Systems Science and Industrial Engineering State University of New York-Binghamton Binghamton, New York