Generalization of the JCGM Approach to Conformity Assessment of a Sample of Products, Materials or Objects

Francesca Pennecchi, Applied Metrology and Engineering, INRiM, Torino, Italia (f.pennecchi@inrim.it)

The JCGM 106:2012 document provides guidelines on how to perform conformity assessment (CA) of a scalar property of interest of a single item (a product, material, object, etc.) based on a Bayesian approach. It gives indications on how to calculate specific and global risks of erroneous decisions for both the consumer (false positive results) and the producer (false negative results), when CA is intended on one item a time.

The work presented here offers a way to extend the application of the JCGM 106 approach to the CA of a finite sample of N items drawn from a common population, leading to a quality assessment of the whole sample. It proposes to calculate first the usual specific and global risks according to the JCGM 106, and then to model the probability of the number of conforming items within the sample by means of appropriate (discrete) probability mass functions (PMFs). Specifically, the proposed model resorts to a Poisson binomial PMF, when the items in the sample are characterized by their specific risks, and to a Multinomial PMF, respectively, when the sample is drawn from a population characterized by corresponding global risks.

The above-mentioned PMFs allow answering questions like: which is the probability that at least a certain number items in the sample are actually conforming, provided that a certain number were found to be out of specification? Which thresholds could be set for false positives and false negatives in order to get a desired quality for a future sample drawn from that population? How would this quality be impacted if the sample size and/or the measurement uncertainty changed?

Application examples of the proposed modelling will be shown at the Workshop.

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Short Biography of Presenting Author

Francesca Pennecchi is a senior researcher at the Istituto Nazionale di Ricerca Metrologica (INRiM, Italy), within the Applied Metrology and Engineering Division. She holds a Degree in Mathematics from the University of Torino (Italy) and a European PhD in Metrology from the Politecnico of Torino (Italy). Participating into several national and international research projects (EMRP, EMPIR, IUPAC/CITAC, and industrial ones), her research activity has been mainly focused on mathematical and statistical methods for uncertainty evaluation, regression analysis and modelling of risks of false decisions in conformity assessment. Recently, she drew her attention to Machine Learning algorithms for metrological applications and to approaches for the harmonization of interlaboratory comparisons of qualitative properties.

She was recently appointed as the chair of the European Metrology Network for Mathematics and Statistics (EMN Mathmet). She is also co-chair of the ENBIS Special Interest Group on Measurement Uncertainty and chair of the UNI/CT016/GL69 “Applicazione dei metodi statistici” of the Italian Standardization Body. She is member of the Eurachem/CITAC Measurement Uncertainty and Traceability Working Group and ISO/TC 69/SC 6/WG 7 Statistical methods to support measurement uncertainty evaluation. She organized three editions (2019, 2021, 2023) of the ENBIS/MATHMET joint Workshop “Mathematical and Statistical Methods for Metrology” (MSMM) and she regularly provides PhD courses on measurement uncertainty evaluation within the PhD course on Metrology of the Politecnico di Torino. She is co-author of more than 70 peer-reviewed papers published on JCR journals (Scopus h-index 16).