2.
Measurement Process Characterization
2.1. Characterization 2.1.2. What is a check standard?


Shortterm or level1 standard deviations from J repetitions 
An analysis of the check standard data is the basis for quantifying
random errors in the measurement process  particularly
timedependent errors.
Given that we have a database of check standard measurements as described in data collection where
$$Y_{kj}(k=1, \,\ldots, \, K, \,\, j=1, \,\ldots, \, J)$$
represents the jth repetition on the kth day, the mean
for the kth day is


Drawback of shortterm standard deviations  An individual shortterm standard deviation will not be a reliable estimate of precision if the degrees of freedom is less than ten, but the individual estimates can be pooled over the K days to obtain a more reliable estimate. The pooled level1 standard deviation estimate with v = K(J  1) degrees of freedom is $${\large s}_1 = \sqrt{\frac{1}{K} \sum_{k=1}^{K} {\large s}_k^2} \,\,\,\, . $$ This standard deviation can be interpreted as quantifying the basic precision of the instrumentation used in the measurement process.  
Process (level2) standard deviation 
The level2 standard deviation of the check standard
is appropriate for representing the process variability. It is computed
with v = K  1 degrees of freedom as:
$${\large s}_{chkstd} = {\large s}_2 = \sqrt{\frac{1}{K1} \sum_{k=1}^{K} \left( \overline{Y}_{k \, \small{\bullet}}  \overline{Y}_{\small{\bullet} \small{\bullet}} \right) ^2}$$ where $$\overline{Y}_{\small{\bullet} \small{\bullet}} = \frac{1}{K} \sum_{k=1}^{K} \overline{Y}_{k \, \small{\bullet}}$$ is the grand mean of the KJ check standard measurements. 

Use in quality control  The check standard data and standard deviations that are described in this section are used for controlling two aspects of a measurement process:  
Case study: Resistivity check standard  For an example, see the case study for resistivity where several check standards were measured J = 6 times per day over several days. 