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Decision Making under Uncertainty on the Basis of Expert Opinion

The risk assessment in many engineering applications is hampered by a lack of hard data. Under these conditions the selection of probability density function (PDF) seems arbitrary. Quite often the data are not only sparse but also vague expert opinion or conflicting. Several non-probabilistic methods have been proposed in the literature to perform a risk assessment under these conditions. We propose to use probabilistic techniques using uncertain PDFs. The uncertainty on the PDF is characterized by treating the parameters in the PDF as random variables. We expand the classical Bayesian updating scheme to make use of vague or imprecise interval data. Each expert opinion is considered to be a random sample from a parent distribution of expert opinions. Consequently, a conflict between experts is accounted for through the likelihood function. The uncertain PDFs can be used in both simulation-based and MPP-based reliability methods. Because of the uncertainty on the PDF of the random variables, the risk or reliability index itself will be a random variable. Design decisions are made on the basis of the risk assessment and an incorrect risk assessment increases the total cost of the design. Since a cost can be associated with either an over or underestimation of the risk, an optimal reliability index can be determined, which minimizes this cost. The probabilistic framework we present in this paper establishes a direct link between the amount and quality of the available data and the optimal reliability estimate. This link allows the decision maker to weigh expected value of additional data collection efforts against the expected optimal reliability index improvement.