A comparison between a probability bounds analysis and a subjective probability approach to express epistemic uncertainties in a risk assessment context – A simple illustrative example

A common approach to reliability and risk assessments is based on using probability models to reflect aleatory uncertainties (i.e. variation in large populations of similar units) and using subjective probabilities to describe epistemic uncertainties about the unknown parameters of the probability models. The use of subjective probabilities for this purpose has, however, been subject to strong criticism: it is argued that the approach provides too precise results when relating these to the information available. The assignments are based on a number of assumptions and proper justification for many of these seems to be lacking. Several alternative approaches have been suggested to meet this critique, including probability bounds analysis (PBA). The purpose of this paper is to compare a PBA with a subjective probability analysis, based on different types of information, covering varying levels and quality of hard data and expert judgments. A simple production assurance example is used to illustrate the differences. The comparison highlights the dependence on assumptions with different levels of justification. The analysis performed also constitutes an illustration of a two-step approach, where a subjective probability approach is followed and accompanied by a PBA approach and where the result of both assessments are presented to the decision-maker.