# Limit of credibility in risk assessments

Jun 5th, 2019

Many users invoke Limit of credibility in risk assessments but rarely discuss what this means.

It is possible to establish limits on the credibility of probabilities estimates based upon the limits of human capabilities and the limits of historical evidence? Limit of credibility in risk assessments, what do we really mean?

Let’s start with a couple statements that may sound like a joke.

## …and there was light

The Big Bang universe creation occurred 1010 years ago, meaning the “history of our universe” is about fourteen billion years old (so, rounded-up 1010years old). That mean a “frequentist” person could think that the “occurrence rate” is once per 10-10 years.

Thus, any yearly frequency smaller than 10-10 really means that the event “occurrence rate” is less likely than our universe! This obviously is our “cosmological” extreme lower bound Limit of credibility in risk assessments.

## Nuclear and chemical industry

In  nuclear probabilistic safety assessments (page 243) researchers think probabilities can be quantified with reasonable certainty down to frequency levels of 10-6 to 10-7/year. Below such values no meaningful uncertainty bands can be given for single events. Therefore, those sources recommend a cut-off frequency of 10-7/year for single events.

Indeed, predictions of most events which require human error frequencies of the order of 10-7 are clearly incredible because the historical data set required to establish such human performance is generally non-existent.

## The no-events scenario associated frequency

Sometimes a time interval can be identified but the evidence indicates that there have been zero occurrences of some particular event (page 294)

If an event has never occurred, it is true that the lower bound for its frequency of occurrence is unknown. However, we can obtain an upper bound by assuming that we can bound from above zero occurrence by one occurrence.

## Expert judgment and Limit of credibility in risk assessments

When data is unavailable, and a probability range needs to be expressed expert judgment is used. We have developed the following tables to help our clients.

## Estimation of large probabilities

 Colloquial vocabulary used to describe the event x occurrence. Event x Frequency equivalent of x N.B.  If these events occur with a known average rate and independently of the time since the last event. Px to see the event next year px min – px max Usually, Almost always Finding at least one container of ice cream in a family freezer. At least one sunny week-end in the next year. ≥1 0.63 – ~1.0 Common, Must be considered, Not always A member of the family gets a cold next year. Getting stuck in a traffic jam for at least 20 minutes next year (exclude commuting). 0,7 – 1 0.5 – 0.63 Not uncommon A person between the age of 18 and 29 does NOT read a newspaper regularly 0.36 – 0.7 0.3 – 0.5 May be, Possibly Getting stuck for more than one hour in traffic (exclude commuting). A celebrity marriage will last a lifetime. 0.23 – 0.36 0.2 – 0.3 Not usually, Occasionally Odds of Dying from Heart Disease or Cancer in the US (1/7) Chance of drawing 1 when drawing a fair dice (1/6=0.16) 0.11 – 0.23 0.1-0.2 Rarely Almost never Never NB: a non expert should stop at this level of scrutiny. Experts can develop more in depth estimates for lower probabilities levels using the next Table 0 – 0.1

## Lower range probabilities

 Likelihood of “rare” Phenomena Event x Return time (years) prob≈frequencies Px to see the even next year px min – px max High Having an income of more than 700kUS\$ in the US in 2017 (1 in 100) Higher bound of likelihood to have a 7.0 or even higher magnitude on the San Andreas Fault line 100 – 10 0.01 – 0.1 (10-2 – 10-1) Moderate Assault by Firearm in the US (237 in 100’000 inhabitants) 1’000 – 100 0.001 – 0.01 (10-3 – 10-2) Low Influenza death (1 in 5’000 to 1 in 1’000) per person An earth tailings dam breaches on Earth per year 10’000 – 1’000 0.0001 – 0.001 (10-4 – 10-3) Very Low Fatal accident at work (1 in 43’500 to 1 in 23’000) per worker Class 5+ nuclear accident on Earth 100’000 – 10’000 0.00001-0.0001 (10-5 -10-4) Extremely Low Person stricken by lightning (1 in 161,856) 1’000’000 – 100’000 0.000001-0.00001 (10-6 -10-5) Credibility threshold Lower likelihoods exist Fatality in Railway accident (travelling in Europe) (0.15 per Billion km) Meteor landing precisely on your house; a major Swiss hydro-dam breaching. N/A Unless data abound, lower values should not be used.

Category: Probabilities, Risk analysis, Risk management

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