Estimation of repeatability and between-method reproducibility using a novel statistical model

Measurement uncertainty is used to describe the quality of a measurement value and ensures the ability of a laboratory to reliably implement quality improvement initiatives. The repeatability and reproducibility (R&R) study is the program most widely used to assess measurement uncertainty. R&R study is based on the assumption of a normal probability distribution of measurement results. However, standard R&R methods are inadequate for evaluating measurement uncertainty in numerous situations involving an insufficiently realistic normality assumption. This study proposes a statistical model for determining the R&R variance for inter-laboratory measurement results. The Expectation Maximization (E-M) algorithm and generalized linear model (GLM) are applied to estimate the repeatability variance, and a developed method is designed for estimating inter-laboratory and reproducibility variance. The findings are employed to evaluate and improve measurement uncertainty in laboratory accreditation.