A modified Bayes' theorem for reliable conformity assessment in industrial metrology. (November 2021)

• Record Type: Journal Article
• Authors: Jetti, Harsha Vardhana; Ferrero, Alessandro; Salicone, Simona
• Is Part Of: Measurement. Volume 184(2021)
• Publication Date: 2021-11
• Subjects: Bayes' theorem -- Industrial metrology -- Consumer risk -- Manufacturer risk -- Deviation -- Systematic -- Random-Fuzzy Variable -- Possibilistic variance; Weights and measures -- Periodicals; Measurement -- Periodicals; Measurement; Weights and measures; Periodicals; 530.8
• DOI: 10.1016/j.measurement.2021.109967
• Languages: English
• ISSNs: 0263-2241

Abstract

Abstract: Numerous papers in the literature recommend the use of Bayes' theorem to merge the available a priori knowledge about a measurand with the measurement result associated to the measurand itself. The obtained a posteriori value should be used in conformity assessment, rather than the measured one, to reduce the risk of erroneous decisions. The assumption behind Bayes' theorem is that the distributions of both the a priori knowledge and the measurements are correct and truly reliable. This means that no deviations or systematic errors in either the manufacturing process or the measuring instrument are considered. The main question is hence whether these assumptions are satisfied or not in the practical industrial cases. And, if they are not satisfied, as it often occurs in the industrial practice how can deviations and systematic errors be considered when applying Bayes' theorem? This paper proposes a solution based on a modified Bayes' theorem using Random-Fuzzy Variables (RFVs) and possibility theory. Different simulations and an experimental case are reported showing the effectiveness of the modified Bayes' theorem in the context of industrial metrology. Highlights: Measuring instrument or manufacturing process may deviate in a practical scenario. Standard Bayes' theorem is not effective or reliable in conformity analysis. Modified Bayes' theorem using RFVs to include the possible deviations. Better results in conformity analysis obtained using the Modified Bayes' theorem.