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Range chart
The X-chart and X-bar chart are useful for detecting bias or drift in a measurement system. These charts may also help to indicate problems with the precision of results from one run to the next, for example if results frequently appear outside of the warning lines. However, these charts do not give any information on the within run precision of measurement results. If the QC material is analysed more than once in a run, the precision of results can be monitored using a range chart.
A range chart is constructed by calculating the difference between the highest and lowest value obtained for the QC material in a run and plotting the values sequentially. It is important that the replicates are completely independent (i.e. the QC material is put through the whole test method each time), and that the range values are obtained from the same number of replicates. The central line plotted on a range chart is usually the mean of the range values. The upper and lower control limits are calculated by multiplying the mean range by the appropriate factor given in the table below [1].
|
Action limits calculated by multiplying the mean range by the appropriate factor for n |
Number of replicate QC results per run (n) |
Lower action limit |
Upper action limit |
2 |
0 |
3.267 |
3 |
0 |
3.574 |
4 |
0 |
2.282 |
5 |
0 |
2.114 |
Shewhart X-bar and R-charts for QC data where 4 portions of the QC material are analysed per run
(Click here for a pdf version of the charts)
The figure above shows plots of mean and range data for a method where the QC material is analysed four times per run. The control limits on both charts were established from previous data for the same method and QC material. Between runs 1 and 10 the method appears to be under control. Between runs 10 and 20, the range values are acceptable but the X-bar chart shows 9 consecutive points on the same side of the target value. This indicates that although the repeatability remains acceptable, there is a positive bias in the measurement results. After run 20 there is a problem with the precision of the results obtained from a number of runs – the range values for runs 21, 23 and 26 are greater than the control limit. The Shewhart chart indicates that the bias that was present in the earlier runs has been corrected.
[1] ISO 8258:1991 Shewhart control charts
Last modified on
30 April 2009.