The Levy-Jennings control charts differ from the Shewhart charts in the estimation of the standard error of the plotted value and the interpretation of the control limits. The former was developed for clinical chemistry assays and the latter was developed for quantitative measurements from industrial production.
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Both charts set control limits as mean +/- 3*SD (SD = standard deviation).
The IR chart (which stands for Individual-Moving Range) determines the standard deviation based on the average moving range. That is determined by calculating the moving range between each sucessive pair of points. If the data is X1, X2, X3, ..., then MR1=|X2-X1|, MR2=|X3-X2|, ... The average moving range (MR_bar) is the average of MR1, MR2, ... , and SD=MR_bar/1.12
The Levey-Jennings chart determines the standard deviation by calculating the overall standard deviation of all the data points.
If a process is stable and the data comes from a normal distribution, and each result is independent of each other, the IR chart and LJ chart should be essentially the same. If the data has large shifts or groupings in the results, in general the MR chart will have narrower limits and be more sensitive.