Teaching uncertainty propagation as a core component in process engineering statistics

• Uncertainty propagation assesses the impact that uncertainty in inputs or parameter can have on outputs.
• Critical aspect in process engineering statistics not addressed in the literature.
• Use in elementary statistics course enabled increased engagement and learning outcomes.
• Can be assessed and taught using multi-mode and project based approaches.

Propagation of uncertainty refers to evaluation of uncertainty in output(s) given uncertainty in input(s). This can be across a physical process, or can be predicted based on a process model. Uncertainty can be propagated analytically, by application of Taylor series variance propagation, or numerically, through repeated Monte-Carlo simulations. Propagation of uncertainty is an important concept in process engineering statistics, which is not currently widely taught. In this paper, an approach is provided for teaching uncertainty propagation as part of a larger process engineering statistics course, applying analytical and numerical propagation principles, including consideration of correlation in inputs. A saline blending practical is used as a case study, with experimental and theoretical determination of how variability in feed pump flows determines variability in outlet conductivity. Based on a class of 132 2nd year Chemical Engineering students, learning outcomes in analytical and numerical linear and non-linear propagation models can be attained and enhanced applicability and engagement within the core statistics course. An engagement survey particularly noted that the students recognised the importance of propagation as a technical capability, but noted difficulties in linking the experimental work to theory of propagation. Overall, propagation of uncertainty allows educators to increase the direct relevance of statistics to process engineering and engage with students through their existing analytical capabilities.

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