An Approach for the Uncertainty Evaluation of the Overall Result from Replications of Measurement: Separately Combining Individual Uncertainty Components According to their 'systematic' and 'random' Effects

In our previous articles, an approach has been proposed for the evaluation of the uncertainty of overall result from multiple measurements. In the approach, uncertainty sources were classified into two groups: the first including those giving same 'systematic' effect on each individual measurement and the second including the others giving 'random' effect on each individual measurement and causing a variation among individual measurement results. The arithmetic mean of the replicated measurements is usually assigned as the value for the overall result. Uncertainty of the overall result is determined by separately evaluating and combining an overall uncertainty from sources of the 'systematic' effect and another overall uncertainty from sources of the 'random' effect. This conceptual approach has been widely adopted in chemical metrology society. In this study, further logical proof with more detailed mathematical expressions is provided on the approach