The long gone, but not forgotten, second issue of the UK MoD’s safety management standard DEFSTAN 00-56 introduced the concept of a qualitative likelihood of Incredible, this is however not just another likelihood category. The intention of the standard writers was that it would be used to capture risks that were deemed effectively impossible to occur, given the assumptions about the domain and system. The category was be applied to those scenarios where the hazard had been designed out, where the design concept had been assessed and it turns out that the posited hazard was just not applicable or where some non-probabilistic technique is used to verify the safety of the system (think mathematical proof). Such a category records that yes, it’s effectively impossible, while retaining the record of assessment should it become necessary to revisit it, a useful mechanism.
A.1.19 Incredible. Believed to have a probability of occurrence too low for expression in meaningful numerical terms.
DEFSTAN 00-56 Issue 2
I’ve seen this approach mangled in a number or hazard analyses were the disjoint nature of the incredible category was not recognised and it was thereafter assigned a specific likelihood that followed on in a decadal fashion from the next highest category. Yes difficulties ensued. The key is that the Incredible is not the next likelihood bin after Improbable it is in fact beyond the end of the line where we park those hazards that we have judged to have an immeasurably small likelihood of occurrence. This, we are asserting, will not happen and we are as confident of that fact as one can ever be.
“Incredible” may be exceptionally defined in terms of reasoned argument that does not rely solely on numerical probabilities.
DEFSTAN 00-56 Issue 2
To put it another way the category reflects a statement of our degree of belief that an event will not occur rather than an assertion as to its frequency of occurrence as the other subjective categories do. What the standard writers have unwittingly done is introduce a superset, in which the ‘no hazard exists’ set is represented by Incredible and the other likelihoods form the ‘a hazard exists’ set. All of which starts to sound like an mashup of frequentist probabilities with Dempster Shafer belief structures. Promising, it’s a pity the standard committee didn’t take the concept further.
The other pity is that the standard committee didn’t link this idea of “incredible” to Borel’s law. Had they done so we would have a mechanism to make explicit what I call the infinite monkey’s safety argument.