Set-valued data analysis for interlaboratory comparisons
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.