Effect of insignificant bias and its uncertainty on the coverage probability of uncertainty intervals: Part 2. Evaluation for a found insignificant experimental bias

This paper continues in studying the coverage probability of uncertainty intervals. It particularly investigates the uncertainty intervals determined in compliance with the GUM and EURACHEM Guide in case of the results uncorrected for the systematic error, since the experimental bias has been found insignificant. The problem is solved for known values of the experimental bias, its standard uncertainty and the overall standard uncertainty. The obtained findings given in graphs and tables show that coverage probability of the uncertainty intervals defined by expanded uncertainty about the uncorrected results can considerably fall below the chosen level of confidence; this depression depends only on the ratio of the bias and the overall uncertainty. The bias uncertainty does not directly influence this depression, it only determines whether the bias is significant or not and thereby determines whether the results will be corrected or not. The paper proposes three methods how to remove this coverage probability reduction: to apply a higher level of confidence in the significance test, to correct the results with the insignificant but too high biases and to compute the uncertainty intervals defined by some type of the uncertainties enlarged with the insignificant bias.