Roger Flage

Probability and Possibility‐Based Representations of Uncertainty in Fault Tree Analysis

Expert knowledge is an important source of input to risk analysis. In practice, experts might be reluctant to characterize their knowledge and the related (epistemic) uncertainty using precise probabilities. The theory of possibility allows for imprecision in probability assignments. The associated possibilistic representation of epistemic uncertainty can be combined with, and transformed into, a probabilistic representation; in this article, we show this with reference to a simple fault tree analysis. We apply an integrated (hybrid) probabilistic-possibilistic computational framework for the joint propagation of the epistemic uncertainty on the values of the (limiting relative frequency) probabilities of the basic events of the fault tree, and we use possibility-probability (probability-possibility) transformations for propagating the epistemic uncertainty within purely probabilistic and possibilistic settings. The results of the different approaches (hybrid, probabilistic, and possibilistic) are compared with respect to the representation of uncertainty about the top event (limiting relative frequency) probability. Both the rationale underpinning the approaches and the computational efforts they require are critically examined. We conclude that the approaches relevant in a given setting depend on the purpose of the risk analysis, and that further research is required to make the possibilistic approaches operational in a risk analysis context.

Uncertainty in Risk Assessment

Explores methods for the representation and treatment of uncertainty in risk assessment In providing guidance for practical decision-making situations concerning high-consequence technologies (e.g., nuclear, oil and gas, transport, etc.), the theories and methods studied in Uncertainty in Risk Assessment have wide-ranging applications from engineering and medicine to environmental impacts and natural disasters, security, and financial risk management. The main focus, however, is on engineering applications. While requiring some fundamental background in risk assessment, as well as a basic knowledge of probability theory and statistics, Uncertainty in Risk Assessment can be read profitably by a broad audience of professionals in the field, including researchers and graduate students on courses within risk analysis, statistics, engineering, and the physical sciences. Uncertainty in Risk Assessment: Illustrates the need for seeing beyond probability to represent uncertainties in risk assessment contexts. Provides simple explanations (supported by straightforward numerical examples) of the meaning of different types of probabilities, including interval probabilities, and the fundamentals of possibility theory and evidence theory. Offers guidance on when to use probability and when to use an alternative representation of uncertainty. Presents and discusses methods for the representation and characterization of uncertainty in risk assessment. Uses examples to clearly illustrate ideas and concepts.

Use of decision criteria based on expected values to support decision-making in a production assurance and safety setting

We consider decision problems related to production assurance and safety. The issue is to what extent we should use decision criteria based on expected values, such as the expected net present value (E[NPV]) and the expected cost per expected number of saved lives (ICAF), to guide the decision. Such criteria are recognised as practical tools for supporting decision-making under uncertainty, but is uncertainty adequately taken into account by these criteria? Based on the prevailing practice and the existing literature, we conclude that there is a need for a clarification of the rationale of these criteria. Adjustments of the standard approaches have been suggested to reflect risks and uncertainties, but can cautionary and precautionary concerns be replaced by formulae and mechanical procedures? These issues are discussed in the present paper, particularly addressing the company level. We argue that the search for such formulae and procedures should be replaced by a more balanced perspective acknowledging that there will always be a need for management review and judgment beyond the realm of the analyses. Most of the suggested adjustments of the E[NPV] and ICAF approaches should be avoided. They add more confusion than value.

Strengthening quantitative risk assessments by systematic treatment of uncertain assumptions

Abstract The results of quantitative risk assessments (QRA) are conditional on the background knowledge on which the assessments are based, including phenomenological understanding, models, data and expert statements used, as well as assumptions made. Risk indices established in the risk assessment, such as individual risk numbers and f–N curves, may have a more or less solid foundation, depending for example on the validity of assumptions made. Poor models, lack of data or simplistic assumptions are examples of potential sources of uncertainty “hidden in the background knowledge” of a risk assessment. These uncertainties need to be reflected in the risk assessment. Recently, a method for treating uncertain assumptions in a QRA was suggested. The method is based on the different settings faced when making assumptions in risk assessments, considering beliefs about assumption deviation, sensitivity of the risk index to changes in the assumption, and the overall strength of knowledge involved. In the present paper we apply, test and adjust the method using a risk assessment of a lifting operation related to the oil and gas industry as a case. We find that an adjusted version of the method provides systematic guidance on how to treat uncertainties in a QRA.

Emerging risk – Conceptual definition and a relation to black swan type of events

The concept of emerging risk has gained increasing attention in recent years. The term has an intuitive appeal and meaning but a consistent and agreed definition is missing. We perform an in-depth analysis of this concept, in particular its relation to black swan type of events, and show that these can be considered meaningful and complementary concepts by relating emerging risk to known unknowns and black swans to unknown knowns, unknown unknowns and a subset of known knowns. The former is consistent with saying that we face emerging risk related to an activity when the background knowledge is weak but contains indications/justified beliefs that a new type of event (new in the context of that activity) could occur in the future and potentially have severe consequences to something humans value. The weak background knowledge among other things results in difficulty specifying consequences and possibly also in fully specifying the event itself; i.e. in difficulty specifying scenarios. Here knowledge becomes the key concept for both emerging risk and black swan type of events, allowing for taking into consideration time dynamics since knowledge develops over time. Some implications of our findings in terms of risk assessment and risk management are pointed out.

Safety constraints applied to an adaptive Bayesian condition-based maintenance optimization model

A model is described that determines an optimal inspection and maintenance scheme for a deteriorating unit with a stochastic degradation process with independent and stationary increments and for which the parameters are uncertain. This model and resulting maintenance plans offers some distinct benefits compared to prior research because the uncertainty of the degradation process is accommodated by a Bayesian approach and two new safety constraints have been applied to the problem: (1) with a given subjective probability (degree of belief), the limiting relative frequency of one or more failures during a fixed time interval is bounded; or (2) the subjective probability of one or more failures during a fixed time interval is bounded. In the model, the parameter(s) of a condition-based inspection scheduling function and a preventive replacement threshold are jointly optimized upon each replacement and inspection such as to minimize the expected long run cost per unit of time, but also considering one of the specified safety constraints. A numerical example is included to illustrate the effect of imposing each of the two different safety constraints.

On treatment of uncertainty in system planning

In system planning and operation considerable efforts and resources are spent to reduce uncertainties, as a part of project management, uncertainty management and safety management. The basic idea seems to be that uncertainties are purely negative and should be reduced. In this paper we challenge this way of thinking, using a common industry practice as an example. In accordance with this industry practice, three uncertainty interval categories are used: ±40% intervals for the feasibility phase, ±30% intervals for the concept development phase and ±20% intervals for the engineering phase. The problem is that such a regime could easily lead to a conservative management regime encouraging the use of existing methods and tools, as new activities and novel solutions and arrangements necessarily mean increased uncertainties. In the paper we suggest an alternative approach based on uncertainty and risk descriptions, but having no predefined uncertainty reduction structures. The approach makes use of risk assessments and economic optimisation tools such as the expected net present value, but acknowledges the need for broad risk management processes which extend beyond the analyses. Different concerns need to be balanced, including economic aspects, uncertainties and risk, and practicability.

An imprecision importance measure for uncertainty representations interpreted as lower and upper probabilities, with special emphasis on possibility theory

Uncertainty importance measures typically reflect the degree to which uncertainty about risk and reliability parameters at the component level influences uncertainty about parameters at the system level. The definition of these measures is typically founded on a Bayesian perspective where subjective probabilities are used to express epistemic uncertainty; hence, they do not reflect the effect of imprecision in probability assignments, as captured by alternative uncertainty representation frameworks such as imprecise probability, possibility theory and evidence theory. In the present article, we define an imprecision importance measure to evaluate the effect of removing imprecision to the extent that a probabilistic representation of uncertainty remains, as well as to the extent that no epistemic uncertainty remains. Possibility theory is highlighted throughout the article as an example of an uncertainty representation reflecting imprecision, and used in particular in two numerical examples that are included for illustration.

Comparing and integrating the NUSAP notational scheme with an uncertainty based risk perspective

Efforts to develop approaches to represent uncertainty in risk assessments follow both quantitative and semi-quantitative lines, where semi-quantitative is here to be understood as quantitative representation supplemented with qualitative assessments of aspects not sufficiently and appropriately captured by the produced numbers. The latter type of approach can be referred to as extended quantitative risk assessment and has parallels with the so-called NUSAP notational scheme of uncertainty and quality in science for policy. In the present paper we analyse the parallels that exist between NUSAP and a general description of risk as conceptualised in the recently published Society for Risk Analysis glossary. In addition to obtaining insights at the fundamental level into different approaches to describe risk, an objective is to explore whether aspects from the NUSAP notational scheme can be used within the context of and to improve current methods for extended quantitative risk assessment consistent with the general description of risk. We conclude that there are strong parallels between the two approaches and that particularly the use of visualisation tools in NUSAP can advantageously be utilised in extended quantitative risk assessments. A short example from the oil and gas industry is used to illustrate how this can be done.

Moving beyond probabilities – Strength of knowledge characterisations applied to security

Many security experts avoid the concept of probability when assessing risk and vulnerabilities. Their main argument is that meaningful probabilities cannot be determined and they are consequently not useful for decision-making and security management. However, to give priority to some measures and not others, the likelihood dimension needs to be addressed in some way; the question is how. One approach receiving attention recently is to add strength of knowledge judgements to the probabilities and probability intervals generated. The judgements provide a qualitative labelling of how strong the knowledge supporting the probability assignments is. Criteria for such labelling have been developed, but not for a security setting. The purpose of this paper is to develop such criteria specific to security applications and, using some examples, to demonstrate their suitability.