A Critical Discussion and Practical Recommendations on Some Issues Relevant to the Nonprobabilistic Treatment of Uncertainty in Engineering Risk Assessment

Abstract

Models for the assessment of the risk of complex engineering systems are affected by uncertainties due to the randomness of several phenomena involved and the incomplete knowledge about some of the characteristics of the system. The objective of this article is to provide operative guidelines to handle some conceptual and technical issues related to the treatment of uncertainty in risk assessment for engineering practice. In particular, the following issues are addressed: (1) quantitative modeling and representation of uncertainty coherently with the information available on the system of interest; (2) propagation of the uncertainty from the input(s) to the output(s) of the system model; (3) (Bayesian) updating as new information on the system becomes available; and (4) modeling and representation of dependences among the input variables and parameters of the system model. Different approaches and methods are recommended for efficiently tackling each of issues (1)-(4) above; the tools considered are derived from both classical probability theory as well as alternative, nonfully probabilistic uncertainty representation frameworks (e.g., possibility theory). The recommendations drawn are supported by the results obtained in illustrative applications of literature.

Which Parameters Are Important? Differential Importance Under Uncertainty

“…Uncertainty about parameters of the aleatory distribution is commonly known as epistemic uncertainty . There is an open debate about whether a probabilistic representation of uncertainty is exhaustive in the presence of deep uncertainties (Helton & Oberkampf, ; Paté‐Cornell, ; Pedroni, Zio, & Couplet, ). For instance, Aven and Zio (, p. 1169) write that “there is a need for developing broader frameworks where we see beyond probability to measure uncertainty.” Such debate cannot be comprised within the present work, where it is assumed that available data and strength of knowledge allow the assignment of a distribution (either prior or posterior) to the parameters of the aleatory distribution.…”

An integrated risk index accounting for epistemic uncertainty in probability risk assessment

“…Using probability distributions to describe it is only a result of biased perspective of decision makers, and might amply the associated uncertainty. 33 Besides, it has been long argued that epistemic uncertainty has some unique features that cannot be handled properly by probability distributions. For example, in uncertainty assessment of nuclear weapons, both presence of positive evident that the weapons will work, and absence of evident they will not work are relevant in the analysis.…”

“…Parametric uncertainty relates to the estimated values of parameters of the PRA model. 8 Usually, it results in a “level-two” uncertainty analysis setting where outer loop simulations sample realizations of variables subject to epistemic uncertainty (denoted by E ), while for each outer loop simulation, inner loop simulations are conducted to sample from the variables subject to aleatory uncertainty, conditioned on the realizations of E (see 33 for details). Various mathematical frameworks have been developed for quantifying and propagating parametric uncertainty, that is, probability theory, evidence theory, possibility theory, probability box, and interval analysis.…”

“…In possibility theory-based methods, parametric uncertainty is represented by assigning a possibility distribution that quantifies the degree of possibility that each value is actually taken by the uncertain parameter. 33 The parametric uncertainty is, then, propagated based on Zadeh’s extension principle to calculate the possibility and necessity measures, which are supposed to bound the probabilistic risk index. 37 Toscani et al 39 applied a possibility theory-based method to consider the parametric uncertainty in a PRA model for the risk of interference between power and signal lines onboard a satellite.…”

The future of risk assessment

“…This is coherent with the model of the world introduced in [10], conditional on the entire body of knowledge and beliefs of the modeler. Note that the formulation in (3) does not restrict the representation of the uncertainty to the classical probabilistic one and alternative representations can be employed [18,22,57,70,150]. This formulation underlines explicitly the role of the background knowledge systematically incorporated in the risk assessment model; it makes it explicit that the risk assessment outcomes are functions of the current state of knowledge, and of the related assumptions made and parameter values assigned.…”