Un Modelo Alternativo para los Estudios de Homogeneidad en la Producción de Materiales de Referencia

Abstract

The proper use of reference materials (RMs) is crucial in testing and calibration laboratories, where homogeneous (ensuring the same property value) and stable materials (Centro Español de Metrología (2012)) are required to validate measurement methods, calibrate equipment, and ensure the validity of results. ISO Guide 35:2017 defines the homogeneity uncertainty (u_{homo}) as the uncertainty associated with the detected heterogeneity both between and within RMs during their production process. It is suggested to estimate this uncertainty using experimental designs and Analysis of Variance (ANOVA). However, the applicability and interpretation of this technique may pose challenges when asymmetric behaviors are observed among the analyzed bottles. Assuming normality can lead to overestimation or underestimation of this uncertainty, potentially resulting in incorrect decisions and costly consequences when accepting or rejecting a batch. This could lead to a loss of trust from clients and even the loss of laboratory accreditation or recognition.

This study proposes an alternative model that employs the Skew-Normal distribution to estimate the effect of random factors among bottles. A shape parameter in the distribution allows quantifying asymmetry or deviations from the central value. Quasi-Newton optimization algorithms (L-BFGSB) were used, and optionally, in case of convergence limitations, the genetic algorithm (NSGA-II) was employed to maximize the likelihood function and find optimal values for μ, s^{2}_{τ} , s^{2}_{e}, and α.

This alternative model aims to assess potential biases affecting method precision and, consequently, the homogeneity of a reference material. The application focused on producing a reference material for elements in water, evaluating the proposed model at different levels of induced homogeneity through gravimetric analysis.

The proposed model incorporates the shape parameter α in the quantification of s^{2}_{τ}, adjusting this estimation without overestimating the variance. It was concluded that this approach allows for uncertainty estimates comparable to traditional techniques (ANOVA and DerSimonian-Lair) and is suitable for cases where the normality assumptions for the effect between bottles are not met. Although it has limitations in the presence of many outliers related to heterogeneity within the bottle, the model proves suitable for its intended purpose.