X-MR Charts

Applications where sample size for process monitoring is n=1.

Measurement is expensive, e.g. destructive testing

Production rate is very slow

Variation within unit (e.g. roll of paper) is negligible
100% automated inspection

The X-MR Chart (or I-MR Chart) is a useful
control chart if the characteristic is independently
and normally distributed.
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If Xi is the measurement obtained during sampling i, then
the Moving Range, MRi,, is given by

MRi = Abs{Xi - Xi-1} = | Xi - Xi-1 |

e.g. MR1 = |X1 - X0|
MR2 = |X2 - X1|
MR3 = |X3 - X2|

X0 may be set at some historical estimate of the process mean.
If X0 is omitted, then the first MR is not calculated.
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