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

Data collection

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).
Short-term 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 short-term (repeatability) standard deviation for the kth occasion is: $${\large s}_k = \sqrt{\frac{1}{J-1} \sum_{j=1}^{J} ( Y_{kj} - \overline{Y}_{k \, \small{\bullet}} ) ^2} \,\,\,\, . $$ 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 level-1 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 short-term 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.
  1. Identification of test item or check standard
  2. Date
  3. Short-term standard deviation
  4. Degrees of freedom
  5. Instrument
  6. Operator
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