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

**The Center Line and Control Limits of a MR Chart are**

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

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

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.