Archives For Categories of risk

When you look at the safety performance of industries which have a consistent focus on safety as part of the social permit, nuclear or aviation are the canonical examples, you see that over time increases in safety tend to plateau out. This looks like some form of a learning curve, but what’s the mechanism, or mechanisms that actually drives this process?

There are actually two factors at play here, firstly the increasing marginal cost of improvement and secondly the problem of learning from rare events. In the first case increasing marginal cost is simply an economist’s way of stating that it will cost more to achieve that next increment in performance. For example, airbags are more expensive than seat-belts by roughly an order of magnitude (based on replacement costs) however airbags only deliver 8% reduced mortality when used in conjunction with seat belts, see Crandall (2001). As a result the next increment in safety takes longer and costs more (1).

The second case is a more subtle version of the first. As we reduce accident rates accidents become rarer. Now one of the traditional ways in which safety improvements occur is through studying accidents when they occur and then to eliminate or mitigate identified causal factors. Obviously as the accident rate decreases this likewise the opportunity for improvement also decreases. When accidents do occur we have a further problem because (definitionally) the cause of the accident will comprise a highly unlikely combination of factors that are needed to defeat the existing safety measures. Corrective actions for such rare combination of events therefore are highly specific to that events context and conversely will have far less universal applicability.  For example the lessons of metal fatigue learned from the Comet airliner disaster has had universal applicability to all aircraft designs ever since. But the QF-72 automation upset off Learmouth? Well those lessons, relating to the specific fault tolerance architecture of the A330, are much harder to generalise and therefore have less epistemic strength.

In summary not only does it cost more with each increasing increment of safety but our opportunity to learn through accidents is steadily reduced as their arrival rate and individual epistemic value (2) reduce.


1. In some circumstances we may also introduce other risks, see for example the death and severe injury caused to small children from air bag deployments.

2. In a Popperian sense.


1. Crandall, C.S., Olson, L.M.,  P. Sklar, D.P., Mortality Reduction with Air Bag and Seat Belt Use in Head-on Passenger Car Collisions, American Journal of Epidemiology, Volume 153, Issue 3, 1 February 2001, Pages 219–224,

Donald Trump

Image source: AP/LM Otero

A Trump presidency in the wings who’d have thought! And what a total shock it was to all those pollsters, commentators and apparatchiks who are now trying to explain why they got it so wrong. All of which is a textbook example of what students of risk theory call a Black Swan event. Continue Reading…

M1 Risk_Spectrum_redux

A short article on (you guessed it) risk, uncertainty and unpleasant surprises for the 25th Anniversary issue of the UK SCS Club’s Newsletter, in which I introduce a unified theory of risk management that brings together aleatory, epistemic and ontological risk management and formalises the Rumsfeld four quadrant risk model which I’ve used for a while as a teaching aid.

My thanks once again to Felix Redmill for the opportunity to contribute.  🙂

Crowely (Image source: Warner Bro's TV)

The psychological basis of uncertainty

There’s a famous psychological experiment conducted by Ellsberg, called eponymously the Ellsberg paradox, in which he showed that people overwhelmingly prefer a betting scenario in which the probabilities are known, rather than one in which the odds are actually ambiguous, even if the potential for winning might be greater.  Continue Reading…


One of the problems that we face in estimating risk driven is that as our uncertainty increases our ability to express it in a precise fashion (e.g. numerically) weakens to the point where for deep uncertainty (1) we definitionally cannot make a direct estimate of risk in the classical sense. Continue Reading…

Inspecting Tacoma Narrows (Image source: Public domain)

We don’t know what we don’t know

The Tacoma Narrows bridge stands, or rather falls, as a classic example of what happens when we run up against the limits of our knowledge. The failure of the bridge due to an as then unknown torsional aeroelastic flutter mode, which the bridge with it’s high span to width ratio was particularly vulnerable to, is almost a textbook example of ontological risk. Continue Reading…

I’ve rewritten my post on epistemic, aleatory and ontological risk pretty much completely, enjoy.