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.

A new fault tree analysis approach based on imprecise reliability model

“…24 And the imprecision D can reflect the amount of experts' information about a basic event where classical reliability theory fails. Furthermore, by comparing several assessments coming from different experts, we can know whether there are conflicts between different experts so that we can adopt some skills to eliminate conflict.…”

Possibility and Evidence-Based Reliability Analysis and Design Optimization

“…One is theoretic development related to the fundamentals of reliability theory, e.g. imprecise reliability (Walley, 1991;Utkin and Coolen, 2007;Kozine and Filimonov, 2000) and fuzzy reliability (Cai et al, 1991a;1991b;1993;Huang et al, 2004;; the other is computational (or algorithmic) development in analysis and the design method, e.g., data fusion technology applied to reliability assessment (Hall and Llinas, 1997;Zhang et al, 2010a;Sun et al, 2008;Yang, 2011a; and optimum design methods (Youn and Choi, 2004b;Youn et al, 2004;Aughenbaugh and Paredis, 2005;Huang et al, 2005a;Limbourg, 2005;Mourelatos and Zhou, 2005;Huang et al, 2006a;2012a). These are illustrated in the sections that follow.…”

“…Following Dempster's work, it was his student, Shafer (1976) and Liu et al (2009) who extended Dempster's probability to the theory of evidence in 1976, including a more thorough explanation of belief functions. The name "Dempster-Shafer theory" was coined by Barnett in a paper which marked the entry of the belief functions into the field of artificial intelligence (Aughenbaugh and Paredis, 2005).…”

“…• Lack of information in input data, small sample size, insufficient information or scarce data (Chen et al, 1999;Mourelatos and Zhou, 2004;Nikolaidis and Haftka, 2001;Huang et al, 2004; • Imprecise data or lack of knowledge Youn and Choi, 2004a;Youn et al, 2004;Aughenbaugh and Paredis, 2005;Huang et al, 2005b;2006d;Limbourg, 2005;Mourelatos and Zhou, 2005) • Large-scale, complex or costly systems (Zhuang et al, 2000) …”

“…They also presented applications of this approach with regard to replacement and maintenance decisions. Aughenbaugh and Paredis (2005) consider imprecise probabilities in order to express clearly the precision with which something is known, on the hypothesis that it is valuable to explicitly represent this imprecision by using imprecise probabilities in engineering design. Then an example and computational experiments involving pressure vessel design problems are carried out using two approaches, both variations of utility-based decision making.…”