Individuals and Moving Range Charts

Another variation of the X-bar and R chart, in this case measuring and plotting individual readings instead of a sample average. The range value is obtained from the current reading and a fixed number of previous readings.

This type of control chart is suitable for calibration or testing situations where it is not practical to create subgroups of items for samples.

The control limits on the individual chart may also contain specification limits (the only chart where this is a feasible practice). In general, avoid using specifications on control charts to allow the team to focus on creating and maintaining a stable process.

Check if the data is normally distributed as the interpretation of X-MR charts will be misleading if the data is not normally distributed. It may take 80 to 100 readings before the averages and limits my stabilize sufficiently to determine if the process is stable. And, X-MR charts will take more readings to detect process shifts than an X-bar and R chart.

To determine the control limits us the following formulas and the factor table below.

$$ \large\displaystyle UC{{L}_{x}}=\bar{X}+{{E}_{2}}\overline{MR}$$

$$ \large\displaystyle LC{{L}_{x}}=X-{{E}_{2}}\overline{MR}$$

n	2	3	4	5
D4	3.27	2.57	2.28	2.11
D3	0	0	0	0
E2	2.66	1.77	1.46	1.29

$$ \large\displaystyle {{E}_{2}}={{A}_{2}}\sqrt{n}$$

The control limits for the range chart are the same as described with the X-bar and R chart.

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Related:

Selecting Control Charts (article)

Introduction to Control Charts (article)

Process Capability (article)