Should non-significant bias be included in the uncertainty budget?

The bias of an analytical procedure is calculated in the assessment of trueness. If this experimental bias is not significant, we assume that the procedure is unbiased and, consequently, the results obtained with this procedure are not corrected for this bias. However, when assessing trueness there is always a probability of incorrectly concluding that the experimental bias is not significant. Therefore, non-significant experimental bias should be included as a component of uncertainty. In this paper, we have studied if it is always necessary to include this term and which is the best approach to include this bias in the uncertainty budget. To answer these questions, we have used the Monte-Carlo method to simulate the assessment of trueness of biased procedures and the future results these procedures provide. The results show that nonsignificant experimental bias should be included as a component of uncertainty when the uncertainty of this bias represents at least a 30% of the overall uncertainty.