analysis geared towards computing a probability of failure). The objective will be to demonstrate a methodology that can add significant value to a more traditional probabilistic analysis by highlighting the impact of epistemic uncertainty on confidence and identifying the most effective means of reducing such uncertainty. Section 2 presents a viewpoint on the role of epistemic uncertainty in probabilistic analysis and some of the factors that help identify whether or not a distinction between reducible and irreducible uncertainty is even important. This section will also review an approach, which has been previously reported in the literature, for computing confidence bounds on reliability predictions. Section 3 presents a proposed methodology whereby variance decomposition is used to address epistemic uncertainty in a probabilistic analysis in order to identify the most effective avenues for gaining more information and improving confidence in the probabilistic predictions. Some previous work has been done to address sensitivity analysis in the presence of both epistemic and aleatory uncertainties (Guo and Du, 2007; Bae et al, 2003, 2006; Helton et al, 2006), but this work focused on the use of evidence theory with interval analysis. The approach proposed here, on the other hand, is more amenable to characterization of epistemic uncertainties using Bayesian posterior distributions, which plays a significant role when addressing “lack of data” uncertainty associated with input distributions. Finally, the proposed methodology is illustrated in Section 4 using as a numerical example the deflection of a statically indeterminate beam, and conclusions are given in Section 5. 2 Probabilistic Analysis with Aleatory and Epistemic Uncertainty In the context of modeling and simulation, a probabilistic analysis addresses variations and/or uncertainties using probability theory, typically by formulating model inputs as random variables. There may be several reasons for performing a probabilistic analysis: to estimate the mean and variance of the model output, to estimate confidence bounds on a model output, to estimate the probability of a response quantity exceeding a given threshold, etc. Probabilistic analysis allows one to account for the fact that, for whatever reason, the actual values of the model inputs are not known exactly. This is often referred to as uncertainty, and two distinct types of uncertainty are commonly recognized. Aleatory uncertainty refers to irreducible uncertainty or “inherent variation.” An example is the variation of material properties among individual specimens in a lot. Epistemic uncertainty is reducible uncertainty, which is the result of having imperfect information. An example is the uncertainty about the mean of a random variable when the mean must be estimated based on 10 observed samples: in this case, collecting additional data will reduce this uncertainty. When conducting a probabilistic analysis, the nature of the uncertainty captured by the probabilistic description of the model inputs will depend on the application. John McFarland and David Riha 418
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