🤖 AI Summary
This paper addresses the statistical analysis challenge of set-valued data (e.g., EMI injection point sets from electronic devices) in inter-laboratory comparisons. Methodologically, it proposes a consensus inference–oriented modeling framework that innovatively integrates Hamming distance to quantify set dissimilarity, Fisher’s noncentral hypergeometric distribution to model deviation counts, and a Bayesian hierarchical model to disentangle inter-laboratory consensus from intra-laboratory variability. Key contributions include: (i) the first application of the noncentral hypergeometric distribution to set-based consensus modeling, enabling statistically rigorous quantification of deviation counts; (ii) simultaneous estimation of a global consensus set and laboratory-specific offsets via hierarchical Bayesian inference; and (iii) substantially improved comparability and reliability of multi-laboratory results. The method is validated on real-world EMC inter-comparison data, demonstrating its effectiveness in identifying robust consensus sets and quantifying intra-laboratory variation.
📝 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.