ENBIS-18 in Nancy

2 – 25 September 2018; Ecoles des Mines, Nancy (France) Abstract submission: 20 December 2017 – 4 June 2018

Bayesian Models for Evaluation of Risks in Conformity Assessment of Multicomponent Materials or Objects

4 September 2018, 10:10 – 10:30

Abstract

Submitted by
Francesca Pennecchi
Authors
Francesca Pennecchi (INRiM, Torino), Ilya Kuselman (Independent Consultant on Metrology, Modiin), Ricardo J. N. B. da Silva (Centro de Química Estrutural, University of Lisboa), Brynn Hibbert (School of Chemistry, Sydney)
Abstract
Documents providing guidance for assessing conformity of an item (entity, object or system) with respect to specified requirements have been published in recent years. The widely-known document JCGM 106 [1] offers a Bayesian approach for evaluation of risks of false decisions in conformity assessment taking into account measurement uncertainty. The probability of accepting the item when it should have been rejected is named ‘consumer’s risk’, whereas the probability of falsely rejecting the item is the ‘producer’s risk’. For a given tested item, such risks are referred to as ‘specific consumer’s risk’ and ‘specific producer’s risk’, respectively. When the item is considered as randomly drawn from a statistical population of such items, corresponding risks are named ‘global consumer’s risk’ and ‘global producer’s risk’, since they characterize the item production globally.

When multicomponent materials, such as medications, alloys, food and clinical samples, or environmental compartments (e.g. ambient air), undergo conformity assessment, even if the assessment is successful for each component of the material batch or lot, the total probability of a false decision (total consumer’s risk or total producer’s risk), concerning the batch or lot as a whole, might still be significant. Modelling of such scenarios is important for understanding conformity assessment risks in customs control, clinical analysis, pharmaceutical industry, environmental control and other fields.

In the IUPAC Project [2], Bayesian models of total risk evaluation are formulated for both cases of independence and correlation of the involved variables (components concentrations and corresponding test results). In the former case, based on the law of total probability, it was shown that total risks can be evaluated as appropriate combinations of the particular risks (i.e. those related to the particular/separate components). In the latter case, evaluation of the risks required modelling the variables by multivariate prior probability density and likelihood function in order to obtain corresponding multivariate posterior distribution from which the risks could be calculated. In these situations, correlation could have a considerable influence on the risks.

Analytical results of examples treated in the Project were calculated in the R programming environment. In parallel, a user-friendly MS-Excel program was developed, based on the same Bayesian approach, but implementing Markov Chain Monte Carlo for quantification of specific risks.

[1] BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP and OIML (2012) JCGM 106:2012, Evaluation of Measurement Data – The Role of Measurement Uncertainty in Conformity Assessment. https://www.bipm.org/en/publications/guides/#gum.
[2] IUPAC Project 2016-007-1-500 (2016) Risk of conformity assessment of a multicomponent material or object in relation to measurement uncertainty of its test results. https://iupac.org/projects/project-details/?project_nr=2016-007-1-500.
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