|
2.
Measurement Process Characterization
2.1. Characterization 2.1.2. What is a check standard?
|
|||
| Short-term or level-1 standard deviations from J repetitions |
An analysis of the check standard data is the basis for quantifying
random errors in the measurement process -- particularly
time-dependent 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 short-term standard deviations | An individual short-term 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 level-1 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 (level-2) standard deviation |
The level-2 standard deviation of the check standard
is appropriate for representing the process variability. It is computed
with v = K - 1 degrees of freedom as:
$${\large s}_{chkstd} = {\large s}_2 = \sqrt{\frac{1}{K-1} \sum_{k=1}^{K} \left( \overline{Y}_{k \, \small{\bullet}} - \overline{Y}_{\small{\bullet} \small{\bullet}} \right) ^2}$$ 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. | ||
