Set-valued data analysis for interlaboratory comparisons

TL;DR

This paper develops statistical tools for analyzing set-valued data in interlaboratory comparisons, using Hamming-distance, noncentral hypergeometric distribution, Bayesian inference, and hierarchical models to improve consensus and variability assessment.

Contribution

It introduces novel methods for set-valued data analysis, including models based on Hamming-distance and Bayesian hierarchical approaches, tailored for interlaboratory comparison contexts.

Findings

Effective modeling of deviations using Fisher's noncentral hypergeometric distribution.

Bayesian inference techniques provide robust analysis of set-valued data.

Hierarchical models quantify within-laboratory effects.

Abstract

This article introduces tools to analyze set-valued data statistically. The tools were initially developed to analyze results from an interlaboratory comparison made by the Electromagnetic Compatibility Working Group of Eurolab France, where the goal was to select a consensual set of injection points on an electrical device. Families based on the Hamming-distance from a consensus set are introduced and Fisher's noncentral hypergeometric distribution is proposed to model the number of deviations. A Bayesian approach is used and two types of techniques are proposed for the inference. Hierarchical models are also considered to quantify a possible within-laboratory effect.