Monte Carlo method for the calibration and measurement capability uncertainty of a water flow standard system

Monte Carlo methods are useful if the probability distributions for input quantities are so various that the probability distributions for measurands cannot be easily obtained. The Monte Carlo methods are useful if the measurands cannot be expressed by mathematical formulas in closed forms, or the sensitivity coefficients for measurands with respect to input quantities are too complicated to succinctly express the sensitivity coefficients. The Monte Carlo method is also useful for validating the measurement uncertainty derived by hands according to GUM. This study utilizes the Monte Carlo method to validate the calibration and measurement capability of a water flow standard system, established by KRISS in Korea, and to validate the calibration report uncertainty. This study proposes three types of Monte Carlo methods. The first one is the Monte Carlo method based on ISO 5168. The second one is the Monte Carlo method combining both GUM and EA-4/02. And the third one is the Monte Carlo method for calibration report uncertainty. The first and second methods deal with absolute calibration. The third method deals with comparison calibration, based on the results by the first and second methods. This study introduces the Monte Carlo method based on ISO 5168. After that, the Monte Carlo method combining both GUM and EA-4/02 is developed. Then, the Monte Carlo method for calibration report uncertainty is explained. Control volume uncertainty is included in the method for calibration report uncertainty. It is because the control volume uncertainty is meaningful only for comparison calibration. This study can be used to validate the CMC uncertainty for the upcoming peer review at KRISS scheduled in 2027. This study also shows that the method combining both GUM and EA/4-02 is equivalent with the method based on ISO 5168 under the assumption that the type B uncertainty factors are independent.