Act of God in probabilistic risk assessment

Dec 9th, 2020

We define an Act of God in probabilistic risk assessment as an event with a probability of occurrence below the general consensus for credibility. In other words it is an unbelievable event that is supposed to be unfathomable “God’s will”.

We can quantify probabilities down to certain frequency levels. As a matter of fact, in our day-to-day practice we consider events probabilities as follows:

down to 10^-5 as credible,
between 10^-5 and 10^-6 as poorly credible, and finally,
below 10^-6 as incredible. This the start of the Act of God realm.

Why do we state that? There are several reasons to this. We will discuss them below.

Cosmological extreme value of probabilities

First of all, below the values above we cannot evaluate meaningful uncertainty bands for single events. Indeed, predictions of most events requiring human error frequencies of the order of 10^-6 or less are clearly incredible. That is simply because the historical data set is generally non-existent. Let’s use an “extreme” thinking to put things in perspective!

The lower limit

The Big Bang universe creation occurred 10¹⁰ years ago. That means the “history of our universe” is about fourteen billion years old. As a result, the creation occurred once in a rounded-up 10¹⁰ years period. That means a “frequentist” person could think that the “occurrence rate” is 1/10¹⁰ years. Thus, any 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.

However, as risk assessors we have to be more humble than that!

For instance, in the Proceedings of the CSNI Workshop on PSA Applications and Limitations, Santa-Fe, New Mexico, 1990 (page 243) researchers stated it is possible to quantify probabilities with reasonable “certainty” down to annual probabilities levels of 10^-6 to 10^-7. Indeed, below such values no one can give meaningful uncertainty bands for single events. Therefore, those sources recommend a cut-off frequency of 10^-7 for single events. Now we are getting near to what we use!

Credible accidents in the process industry

The process industry and other industries where major accidents/events are a concern define credible accidents. They are those:

“which are within the realm of possibility (i.e., probability higher than 10^-6/yr) and
have a propensity to cause significant damage (at least one fatality)”.

Interestingly, seismic, geological and other geo-sciences oftentimes use the threshold value of 10^-5 to define “maximum credible events”. Now we are spot-on!

What to do if your model or simulation delivers very low probabilities

Let’s suppose you use a mechanical model to evaluate probabilities. For instance finite elements or other. In addition, at the end of your evaluation you derive probabilities of failure below say 10^-5. Please stop right there! Go back to your uncertainties, review everything. Even if everything seems perfect, do not report anything lower than 10^-5. Likely your model is too perfect to be true.

Remember that, for example, top class hydro-dams have proven to have a probability of failure around 10^-5 to 10^-6. In addition, class 5+ nuclear accidents do occur at around 10^-4/year reactor.

What to do if a consultant or a peer delivers risk assessment with very low probabilities.

There are numerous examples of preposterous statements conveyed verbally or in writing by “experts” that do not understand the limits discussed above.

This happens for both modeled-simulated evaluations as well as semi-empirical ones. Thus, if you use those values, your position will not be a good one. That is especially if you end-up in court in the aftermath of an accident.

If a consultant comes up with such a value, the best advice is to fire him or her before they get you into trouble.