Risk Definition

[Ciaci]

Hi,
the risk R can be estimated by the formula:
R = M*P
where M is the Magnitude and P is the Frequency.
I have two questions now:
1. Does the magnitude depends on the objective of the Analysis, if the Analyisis has as objective the Life Safety, than the M can be quantified in death, if the objective is for example the business continuity, then the Magnitude can be quantified in money. Is it correct?
2. Can the fact that Magnitude and frequency of events with the same probability are inversely proportional be related with the Zipf law?

 

[IRstuff]

Your equation is an expected value calculation and can be applied to anything, including Lotto.

not sure what you are asking in 2); there is no rational basis for assuming that Zipf Law applies, particularly since there are other distributions that supposedly outperform it

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[zeusfaber]

1. Conceptually, yes. You often see magnitude expressed in terms of cost or time.

2. "Magnitude and frequency of events with the same probability are inversely proportional". Read that slowly, checking your understanding of each of the terms you use and decide whether you still want to accept it as fact. Then have a look at how the Zipf law works - in particular, count the number of variables it deals with and decide whether it's a good tool for relating two independent variables.

In practice, multiplying deaths by frequency turns out to be much harder and less useful than you might expect because:
[ul]
[li]Estimating frequency of very rare events with any accuracy requires a lot of data that you'd like to hope you didn't have[/li]
[li]"Deaths" is a bit of a blunt measure too.[/li]
[/ul]
What's often done instead is to create an arbitrary scale for each of Magnitude and Frequency, both loosely attached to the quantitative measure, but usually in a logarithmic sense (it may be this logarithmic measure that you were hinting at in (2) - and quantised into buckets about an order of magnitude apart. Instead of trying to calculate frequency and expected number of deaths precisely, you simply estimate which bucket each lies within.

So a probability scale might have buckets that range between 6:"happens a couple of times a week in our factory", 5:"Happens about once a month", 4:"Once a year", 3:"once every ten years", 2: "hundred years", 1: "thousand years" ...

and the associated magnitude scale (for a safety risk) might be 1: "Needs a few minutes self-care", 2:"Needs time off work", 3:"Needs to be reported to outside agency but full recovery expected", 4:"Multiple reportable, or one Permanently disabling", 5:"Multiple permanent disabilities or a single death", 6:"2-10 deaths", 7:"large numbers of deaths"

It's much easier to place most eventualities onto this sort of scale than it is to quantify things exactly and, since the purpose of the exercise is almost always to highlight the risks that most deserve attention, the fact that the risk score no longer has any meaningful units doesn't really matter. As long as everybody appreciates that the scales are logarithmic, so a difference between risk scores of 2 or 3 is a really big deal.

When dealing with safety risk, some people deliberately bias the magnitude scale to give extra weight to high consequence accidents to mirror public bias against such events.

A.