Uncertainty Calculations
No measurement is ever perfectly exact, there is always some degree of doubt or variability. This is known as measurement uncertainty. Understanding and accounting for this uncertainty is critical as it directly affects the confidence we can place in calibration results. Without properly evaluating uncertainty, even the most precise measurements could lead to incorrect conclusions.
Measuring Uncertainty
Measurement uncertainties are a fundamental element in metrology, especially when it comes to calibrating weights to ensure compliance with standards such as ASTM. Measurement uncertainty represents the margin of error associated with a measurement, and it is essential to assess the reliability of the results. When calibrating a weight, the objective is to determine whether the weight conforms to a given class by considering both its measured value (conventional value) and the associated uncertainty.
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Principles of conformity and non-conformity
For a weight to be declared compliant with a specific class (ASTM, OIML, NIST) the sum of the conventional value of the weight correction and its measurement uncertainty must be less than the tolerance specified for that class. In other words, even considering the uncertainty, the weight must not exceed the tolerable limit defined by the specified class
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Measures in conformity
The ASTM standard defines strict tolerances for each class. For ASTM Class 1, for example;
The tolerance for a 100 g weight is ± 0.25 mg.
If for this weight we obtain following calibration a conventional correction value of 0.010 mg and the total measurement uncertainty is 0.080 mg, we must add these two values ​​to determine if the weight is compliant.
In this case, the sum is: 0.010mg (conventional value of the correction) + 0.080mg (uncertainty) = 0.090mg
The result is therefore compliant, because it remains lower than the tolerance of the weight under ASTM 1 which is 0.25mg.
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Measures in non-compliance
On the other hand, if the conventional value of correction of the weight of 100 g is 0.240mg and the measurement uncertainty was still 0.080mg,
The sum would be: 0.24mg (conventional value of the correction) + 0.080mg (uncertainty) = 0.320mg.
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In this case, the weight would not comply with ASTM class 1, because the sum of the correction and the uncertainty exceeds the tolerance of ± 0.25mg.
The tolerance tables can be found here