A statistical approach for estimating intervals of certification or biases of facilities or measurement systems including uncertainties is set forth based on M×N-order level testing, which is defined as M repetitions of the same N-order level experiment in M different facilities or in the same facility with M different measurement systems. In the absence of reference values, the mean facility or measurement system is used for assessing intervals of certification or biases. Certification or biases of facilities or measurement systems are defined as processes for assessing probabilistic confidence intervals for facilities or measurement systems for specific tests, data reduction equations, conditions, procedures, and uncertainty analysis. Similarly, subgroup analysis is performed for isolating and assessing levels of differences due to use of different model sizes (scale effects) or measurement systems. An example is provided for towing tank facilities for resistance tests using standard uncertainty analysis procedures based on an international collaboration between three facilities. Although the number of facilities are at a minimum, the results demonstrate the usefulness of an approach and support recommendation of future collaborations between more facilities. Knowledge of intervals of certification or biases is important for design, accrediting facilities or measurement systems, and CFD validation.

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