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The X-bar chart for Reproducibility analyzes whether the average for the selected parts from each Appraiser is within the expected variability of these averages. In other words, it detects whether the differences between Appraiser averages is an indication of Appraiser bias, or an expected variation due to equipment.
If the equipment error, as represented on the Combined Appraiser Repeatability Range (or Sigma) chart, is in control, then repeat is an appropriate estimate of the variation from trial to trial. Trial averages, therefore, should fall within the variability reflected by:
so long as there are no outside influences affecting the trial measurements, such as Appraiser bias. This is the basis for the Reproducibility X-bar control chart, whose calculations are shown below.
The Range chart for Reproducibility analyzes the variability in Appraiser averages for each part. As such, it may be used to identify whether the reproducibility is in a state of statistical control. If control is not exhibited, then the estimate of reproducibility may not be valid. Points out of control indicate that the variability in average measurements between Appraisers is affected by part bias.
Sigma charts are used instead of Range charts when the subgroup sample size (in this case, the number of Appraisers) is more than ten. This is due to the decreasing efficiency of the range as an estimate of the standard deviation for larger subgroup sizes.