Evaluation of probabilities of false decisions at conformity assessment of test results

The JCGM 106 document [1] provides guidance and procedures for assessing conformity of an item (entity, object or system) with a specified requirement. Such requirement typically takes the form of a tolerance interval, i.e. an interval of permissible/conforming values of a measurable property of the item. Beside tolerance intervals, also an acceptance interval can be applied [2], depending on the measurement uncertainty and the requirements of the decision rule. In fact, since, typically, the item property, i.e. the measurand, is not directly observable, “… an accept/reject decision is based on observable data (measured quantity values, for example) that lead to an inference regarding the possible values of a non-observable measurand. Because of uncertainty in measurement, there is always the risk of incorrectly deciding whether or not an item conforms to a specified requirement based on the measured value of a property of the item” [1]. In this framework, the ‘consumer’s risk’ is the probability of accepting the item when it should have been rejected, that is, the probability that the measured value falls within the acceptance interval whereas the true value of the measurand is outside the tolerance interval (the ‘producer’s risk’ being defined the other way round).

In order to calculate such risks, the basic idea is to resort to probability theory: the knowledge about the measurand can be expressed in terms of a probability density function (pdf), which, according to the Bayes theorem, combines prior information on the measurand and new knowledge acquired during the measurement. Therefore, the above-mentioned probabilities of false decisions can be calculated by integrating such pdf on the relevant intervals of the measurement results and the true property values of the item, respectively.

In this vein, a guide for investigating out-of-specification test results of chemical composition was recently published [3] and a new IUPAC project [4] was started with the purpose of developing guidelines for evaluating the probability of false decisions in conformity assessment of multicomponent materials or objects.
References

1. JCGM 106 Guide: Evaluation of measurement data - The role of measurement uncertainty in conformity assessment, 2012.
2. EURACHEM/CITAC Guide: Use of uncertainty information in compliance assessment, First Edition 2007.
3. IUPAC/CITAC Guide: Investigating out-of-specification test results of chemical composition based on metrological concepts, 2012.
4. IUPAC Project 2016-007-1-500 (2016) Risk of conformity assessment of multicomponent material or object in relation to measurement uncertainty of its test results, http://iupac.org/project/2016-007-1-500