|
2.
Measurement Process Characterization
2.2. Statistical control of a measurement process 2.2.3. How is short-term 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). | ||
| 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.
|
||
