The Value of Using Imprecise Probabilities in Engineering Design

Abstract

Engineering design decisions inherently are made under uncertainty. In this paper, we consider imprecise probabilities (i.e. intervals of probabilities) to express explicitly the precision with which something is known. Imprecision can arise from fundamental indeterminacy in the available evidence or from incomplete characterizations of the available evidence and designer's beliefs. Our hypothesis is that, in engineering design decisions, it is valuable to explicitly represent this imprecision by using imprecise probabilities. We support this hypothesis with a computational experiment in which a pressure vessel is designed using two approaches, both variations of utility-based decision making. In the first approach, the designer uses a purely probabilistic, precise best-fit normal distribution to represent uncertainty. In the second approach, the designer explicitly expresses the imprecision in the available information using a probability box, or p-box. When the imprecision is large, this p-box approach on average results in designs with expected utilities that are greater than those for designs created with the purely probabilistic approach. In the context of decision theory, this suggests that there are design problems for which it is valuable to use imprecise probabilities.

Uncertainty in Through-Life Costing–-Review and Perspectives

“…Some researchers have used this representation to incorporate the uncertainty caused by lack of knowledge and variability in engineering design and risk analysis [96], [97]. The epistemic uncertainty is characterized by the interval bounds/sets of cdf and variability is characterized by the cdf.…”

Design Optimization with Imprecise Random Variables

“…Imprecise probabilities have previously been considered in reliability analysis [19,20,21] and engineering design [22,23,24]. Aughenbaugh and Herrmann [25,26,27] have compared techniques using imprecise probabilities to other statistical approaches for making reliabilitybased design decisions.…”

Comparing Stochastic Design Decision Belief Models: Pointwise versus Interval Probabilities

“…For example, credal sets have been used to design a pressure vessel with a new material (representing uncertain design conditions). In this pressure vessel design case, it was shown that where the imprecision is large, the credal sets outperformed the classic pointwise probability distribution representation method [6].…”