Comparing the Robustness of Statistical Estimators of Proficiency Testing Schemes for a Limited Number of Participants

Abstract

This study aims at developing models in analyzing the results of proficiency testing (PT) schemes for a limited number of participants. The models can determine the best estimators of location and dispersion using unsatisfactory results as a criterion by combining: (a) robust and classical estimators; (b) kernel density plots; (c) Z-factors; (d) Monte Carlo simulations; (e) distributions derived from the addition of one or two contaminating distributions and one main Gaussian. The standards ISO 13258:2015, ISO 5725:2:1994, and EN ISO/IEC 17043:2010 are the basis of the analysis. The study describes an algorithm solving the optimization problem for (a) Gaussian, bimodal or trimodal distributions; (b) participating labs from 10 to 30; (c) fraction of the contaminating population up to 0.10; (d) variation coefficient of the main distribution equal to 2; (e) equal standard deviations of all the distributions, and provide figures with the optimal estimators. We also developed a generalized algorithm using kernel density plots and the previous algorithm, which is not subject to restrictions (b)–(e) and implemented in the results of a PT for the 28-day strength of cement with 12–13 participants. Optimal estimators’ figures and the generalized algorithm are helpful for a PT expert in choosing robust estimators.