Tag Archive | X-MR Charts

X-MR Charts

Applications where sample size for process monitoring is n=1

  • 100% automated inspection and measurement
  • production rate is very slow
  • repeatability of measurement is negligible
  • variation within unit (e.g. roll of paper) is negligible

The X-MR Chart (or I-MR Chart) is a useful control chart if the characteristic is independently and normally distributed.

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 MR1 is not calculated.

The Center Line and Control Limits of a X Chart are

X-MR Charts1

X-MR Charts1

The Center Line and Control Limits of a MR Chart are

X-MR Charts2

X-MR Charts2

Example

The viscosity of an aircraft primer is an important quality characteristic.  Production is in batches, with a very slow production rate.  Hence, only 1 sampling is performed per batch.The viscosity over 15 batches of primer is reviewed to determine if the process is in-statistical-control.

X-MR Charts3

X-MR Charts3

Smart SPC Analyst’s—Statistic—I-MR Chart

X-MR Charts4

X-MR Charts4

The moving ranges are correlated, i.e. they are dependent on the current and previous data points (X0 and Xi-1).
This correlation may induce a pattern of runs or cycles on the MR Chart.
Avoid or ignore secondary indicators of instability.