Introduction

This chapter gives a brief introduction to the relatively new and expanding field of uncertainty analysis. Fundamental concepts are introduced, but theorems will not be proved here. Since uncertainty analysis is effectively dependent on computer support, the models used in uncertainty analysis are discussed in relation to simulation methods. A good elementary introduction to simulation is found in the book of Ross [Ross, 1990].

Uncertainty analysis was introduced with the Rasmussen Report WASH-1400 [NRC, 1975] which, as we recall, made extensive use of subjective probabilities. It was anticipated that the decision makers would not accept a single number as the probability of catastrophic accident with a nuclear reactor. Instead a distribution over possible values for the probability of a catastrophic accident was computed, using estimates of the uncertainty of the input variables. Since this study uncertainty analyses are rapidly becoming standard for large technical studies aiming at consensus in areas with substantial uncertainty. The techniques of uncertainty analysis are not restricted to fault tree probability calculations, rather they can be applied to any quantitative model. Uncertainty analysis is commonplace for large studies in accident consequence modeling, environmental risk studies and structural reliability.

Mathematical formulation of uncertainty analysis

Mathematically uncertainty analysis concerns itself with the following problem. Given some function M(X1, …, Xn) of uncertain quantities X1,…, Xn, determine the distribution of G on the basis of some information about the joint distribution of X1, …, Xn.