2.
Measurement Process Characterization
2.3. Calibration 2.3.3. What are calibration designs? 2.3.3.3. Uncertainties of calibrated values


Repeatability standard deviation comes from the data of a single design 
The repeatability standard deviation of the instrument
can be computed in two ways.


A more reliable estimate comes from pooling over historical data 


Level2 standard deviation is estimated from check standard measurements  The level2 standard deviation cannot be estimated from the data of the calibration design. It cannot generally be estimated from repeated designs involving the test items. The best mechanism for capturing the daytoday effects is a check standard, which is treated as a test item and included in each calibration design. Values of the check standard, estimated over time from the calibration design, are used to estimate the standard deviation.  
Assumptions  The check standard value must be stable over time, and the measurements must be in statistical control for this procedure to be valid. For this purpose, it is necessary to keep a historical record of values for a given check standard, and these values should be kept by instrument and by design.  
Computation of level2 standard deviation 
Given K historical check standard values,
$$ C_1, \, C_2, \, \ldots , \, C_K $$
the standard deviation of the check standard values is computed as $$ {\large s}_C = {\large s}_2 = \sqrt{\frac{1}{K1} \sum_{k=1}^{K} \left( C_k  \overline{C}_{\small{\bullet}} \right)^2} $$ where $$ \overline{C}_{\small{\bullet}} = \frac{1}{K} \sum_{k=1}^{K} C_k $$ with degrees of freedom \( \nu = K  1 \). 