Short note - adequate trust, human-capacity-factor, probability-distribution-function of human non-failure and its entropy

This note is an extension, a generalisation of and an attempt to quantify, on the probabilistic basis, the message of the recent Kaindl and Svetinovic (2019) publication Avoiding Undertrust and Overtrust. The author of the present analysis addresses some important aspects of the human-in-the-loop problem for safety-critical missions and situations, in which trust can be viewed as an essential part of the human-capacity-factor (HCF). This factor, as has been recently suggested, should be evaluated vs. mental workload (MWL), when there is a need to assure a successful and safe outcome of a particular human effort, such as, e.g., an aerospace mission or an extraordinary situation. The double exponential probability distribution function (DEPDF) for the random HCF is revisited. It is shown particularly that the entropy of this distribution, when applied to the trustee (a human, a technology, a methodology or a concept), can be viewed as an appropriate quantitative characteristic of the propensity of a decision maker to an under-trust or an over-trust judgment and, as a consequence of that, to the likelihood of making a mistake or an erroneous decision.