A general Monte-Carlo approach to consider a maximum admissible risk in decision-making procedures based on measurement results

Abstract

According to the standards, decision-making procedures generally consider both a threshold that should not be exceeded and the measurement uncertainty that is associated to the measurement result. However, the general indications given in the Standards, in their examples, refer to the particular case when the measurand distributes according to a normal PDF. But a generalization to other cases is not considered and is not straightforward. In a previous paper, the Authors proposed a decision-making procedure which not only considers the measurement uncertainty and the threshold, but also considers a Maximum Admissible Risk. The proposed procedure leads to decisions taken with a risk of a wrong decision lower than the given Maximum Admissible Risk. In particular, closed-form formulas were derived under specific assumptions for the distributions of the measured values. Hence, the aim of this paper is to generalize the proposed decision rule and method for setting acceptance and rejection limits, by applying the Monte-Carlo method. In this way, it can be generally applied, even when the distribution associated to the measurement result is not a priori known in closed form.