Risk Assessment. Marvin Rausand

Risk Assessment

that the (unknown) state of nature is images

, when we know that we have got the evidence images

In our daily language, likelihood is often used with the same meaning as probability, even though there is a clear distinction between the two concepts in statistical usage. In statistics, likelihood is used, for example, when we estimate parameters (maximum likelihood principle) and for testing hypotheses (likelihood ratio test).

Remark 2.5 (The term likelihood)

In the first part of this chapter, we have used the word likelihood as a synonym for probability, as we often do in our daily parlance. The reason for this rather imprecise use of the word “likelihood” is that we wanted to avoid using the word “probability” until it was properly introduced – and because we wanted to present the main definitions of risk concepts with the same wording that is used in many standards and guidelines.

2.4.2 Controversy

In risk analysis, it is not realistic to assume that the events are repeatable under essentially the same conditions. We cannot, for example, have the same explosion over and over again under the same conditions. This means that we need to use the Bayesian approach. Although most risk analysts agree on this view, there is an ongoing controversy about the interpretation of the subjective probability. There are two main schools:

1 (1) The first school claims that the subjective probability is subjective in a strict sense. Two individuals generally come up with two different numerical values of the subjective probability of an event, even if they have exactly the same knowledge. This view is, for example, advocated by Lindley (2007), who claims that individuals have different preferences and hence judge information in different ways.

2 (2) The second school claims that the subjective probability is dependent only on knowledge. Two individuals with exactly the same knowledge always give the same numerical value of the subjective probability of an event. This view is, for example, advocated by Jaynes (2003), who states:A probability assignment is “subjective” in the sense that it describes a state of knowledge rather than any property of the “real” world but is “objective” in the sense that it is independent of the personality of the user. Two rational human beings faced with the same total background of knowledge must assign the same probabilities [also quoted and supported by Garrick (2008)].

The quotation from Jaynes (2003) touches on another controversy: that is, whether the probability of an event images is a property of the event images , the experiment producing images , or a subjective probability that exists only in the individual's mind.

The mathematical rules for manipulating probabilities are well understood and are not controversial. A nice feature of probability theory is that we can use the same symbols and formulas whether we choose the frequentist or the Bayesian approach, and whether or not we consider probability as a property of the situation. The difference is that the interpretation of the results is different.

Remark 2.6 (Objective or subjective?)

Some researchers claim that the frequentist approach is objective and therefore the only feasible approach in many important areas, for example, when testing the effects of new drugs. According to their view, such a test cannot be based on subjective beliefs. This view is probably flawed because the frequentist approach also applies models that are based on a range of assumptions, most of which are subjective.

2.4.3 Frequency

When an event images occurs more or less frequently, we often talk about the frequency of images rather than the probability of images . Rather than asking “What is the probability of event images ,” we may ask, for example, “How frequently does event images occur?”

Fatal traffic accidents occur many times per year, and we may record the number images of such accidents during a period of length images . A fatal traffic accident is understood as an accident where one or more persons are killed. The frequency of fatal traffic accidents in the time interval images is given by

(2.6) equation

The “time” images may be given as calendar time, accumulated operational time (e.g. the accumulated number of hours that cars are on the road), accumulated number of kilometers driven, and so on.

In some cases, we may assume that the situation is kept unchanged and that the frequency approaches a constant limit when images . We call this limit the rate of the event images and denote it by images :

(2.7) equation

In the frequentist interpretation of probability, parameters like images have a true, albeit unknown value. The parameters are estimated based on observed values, and confidence intervals are used to quantify the variability in the parameter estimators.

Models and formulas for the analysis may be found in Appendix A.

2.5 What are the Consequences?

The third question in our definition of risk introduces the term consequences. A consequence involves specific damage to one or more assets and is also called adverse effect, negative effect, impact, impairment, or loss.

ISO Guide 73 defines consequence as “outcome of an event affecting objectives,” in line with their definition of risk. The term harm is used in several important standards, including ISO 12100. Their definition of harm is “physical injury or damage to health,” limiting the definition only to cover people. This is in line with the objectives of the standard. In this book, no distinction is made between harm and consequence, and we define it more generally as follows:

Definition 2.27 (Harm/consequence)

Injury or damage to the health of people, or damage to the environment or other assets.

2.5.1 Assets

To answer the third question in the triplet definition of risk “what are the consequences?” we first have to identify who – or what – might be harmed. In this book, these “objects” are called assets.

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