Uncertainty in risk engineering: concepts
Overview
A management buzzword that has seen increasing use in the past decade is VUCA: Volatility, Uncertainty, Complexity and Ambiguity. These issues are very relevant to risk management in large sociotechnical systems. How can uncertainty and ambiguity be described, propagated through risk models, presented to decisionmakers?
This submodule covers the following topics:
aleatory, epistemic and valuerelated categories of uncertainty
the objectives of uncertainty modelling
different levels of integration of uncertainty modelling in risk assessment
the propagation of uncertainty through risk models to characterize output uncertainty
This submodule is a part of the risk management module.
Learning objectives
Upon completion of this submodule, you should be able to:
Understand probabilistic modelling and uncertainty propagation
Know when probabilistic and possibilistic uncertainty representations should be used
Know how to combine probabilistic and possibilistic representations in a single model and propagate uncertainties
Understand use of results for decisionmaking
Course material
Uncertainty in risk engineering: concepts 

Python notebook on uncertainty propagation 
In these course materials, applications are presented using the NumPy, SciPy and statsmodels libraries for the Python programming language. We have some material on getting started with Python that explains how to install Python on your computer or try out our computational notebooks using free online services.
Quantitative uncertainty assessments have the following objectives:
understand the influence of uncertainties, which can help determine what is needed to reduce the level of uncertainty, such as undertaking additional measurements, improving your models or modeling or further research efforts
qualify or accredit a model or a method of measurement (“this is of sufficient quality for this purpose”)
influence design, by allowing system designers to compare the relative performance of different design options (for example to optimize the choice of equipment size, operating temperature and pressure, materials, maintenance policy, operating procedure)
compliance, to provide evidence that demonstrates the system’s compliance with explicit criteria or regulatory thresholds (for example in the level of safety risk, in the amount of pollution generated, in variations in product weight or size)
There are five levels of integration of uncertainty in risk assessment, presented from most basic to most sophisticated (and costly to implement):
Integration level 0 consists of undertaking a hazard identification process, and determining whether a risk is present or not (for example, does my product need to be classified as carcinogenic or not).
Integration level 1 is a worstcase approach, which consists of analyzing the worst possible outcome that could arise as a result of an accident (for instance the maximum number of people killed) and planning for that outcome. This is the approach used in emergency planning.
Integration level 2 is a slight modification of level one, and consists of identifying the plausible worst case or plausible upper bound on losses. For instance, you may be asked to estimate the “maximal probable flood” or the “maximal credible earthquake”. The notion of “credible” may be specified in more detail, such as “once in a thousand years”. This type of assessment is regularly used by the insurance industry, with concepts such as the “maximum foreseeable loss”.
Integration level 3 involves the use of best estimates, which amounts to identifying the median of the loss distribution (there is 50% chance that losses will be larger than this value). This approach is only useful when uncertainty levels are low, so extreme losses are not very different from average losses.
Integration level 4 is probabilistic risk assessment, which involves estimating the probability distribution of each input parameter in your accident model, propagating uncertainty through the model using Monte Carlo methods, and examining the entire output probability distribution (both the most likely loss, and probabilities of exceeding some specific quantile of the loss distribution).
Other resources
We recommend the following sources of further information on this topic:
FonCSI report Literature review of methods for representing uncertainty, by E. Zio & N. Pedroni (2013)
The Understanding uncertainty web site (Cambridge University)
Risk Lab, a science gallery of experiments related to risk and its perception
Photo credits: Louis Vest, CC BYSA
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