2.
Measurement Process Characterization
2.2. Statistical control of a measurement process 2.2.3. How is shortterm variability controlled?


Case study: Resistivity  A schedule should be set up for making measurements with a single instrument (once a day, twice a week, or whatever is appropriate for sampling all conditions of measurement).  
Shortterm standard deviations  The measurements are denoted $$Y_{kj}(k=1, \,\ldots, \, K, \,\, j=1, \,\ldots, \, J)$$ where there are J measurements on each of K occasions. The average for the kth occasion is: $$\overline{Y}_{k \, \small{\bullet}} = \frac{1}{J}\sum_{j=1}^{J} Y_{kj}$$ The shortterm (repeatability) standard deviation for the kth occasion is: $${\large s}_k = \sqrt{\frac{1}{J1} \sum_{j=1}^{J} ( Y_{kj}  \overline{Y}_{k \, \small{\bullet}} ) ^2} \,\,\,\, . $$ with (J  1) degrees of freedom.  
Pooled standard deviation  The repeatability standard deviations are pooled over the K occasions to obtain an estimate with K(J  1) degrees of freedom of the level1 standard deviation $${\large s}_1 = \sqrt{\frac{1}{K} \sum_{k=1}^{K} {\large s}_k^2} \,\,\,\, . $$ Note: The same notation is used for the repeatability standard deviation whether it is based on one set of measurements or pooled over several sets.  
Database 
The individual shortterm standard deviations along with
identifications for all significant factors are recorded
in a file. The best way to record this information is by using
one file with one line (row in a spreadsheet) of information
in fixed fields for each group. A list of typical entries follows.
