Measurement uncertainty evaluation in analytical chemistry: Investigating the linearity assumption using an enhanced spreadsheet approach.

Measurement uncertainty plays an important role in conformity assessment and regulatory decision-making in analytical chemistry. Kragten spreadsheet method rely on the assumption that the measurement model is locally linear. However, many chemical measurement models that involve the ratio of input quantities may violate this assumption, leading to potential underestimation of measurement uncertainty. Understanding the impact of non-linearity, and consequently the asymmetric output distribution, is essential to ensure reliable uncertainty estimates and avoid false decisions regarding conformity/non-conformity assessment. This study investigated three commonly used measurement models involving the ratio of input quantities, employing an enhanced Kragten spreadsheet to evaluate linearity assumptions. Deviations from linearity were identified by comparing forward and backward sensitivity coefficients and by analyzing relative differences in uncertainty estimates. Monte Carlo simulations confirmed that non-linear models produce asymmetric output distributions, affecting the accuracy of 95 % coverage intervals. In all measurement models, significant discrepancies were found between intervals calculated by the Kragten method and those obtained by Monte Carlo simulation, particularly at input uncertainties exceeding 15 %. These findings were confirmed by comparing the probabilities of extreme values falling below the lower bounds or above the upper bounds of the expected coverage intervals. The enhanced Kragten approach provides a practical and accessible tool for detecting non-linearity in spreadsheet-based uncertainty evaluations. By identifying cases where the traditional linear assumption fails, this method supports more accurate risk assessments and enhances the reliability of conformity decisions in analytical practice.