An XmR chart (aka Shewhart’s Control Chart aka ImR chart) is a chart where the control limits are calculated from the moving average range.

## Use XmR Control Charts When:

- When you have continuous data.
- When you have subgroups of size = 1.
- You use the ImR (XmR) chart only when logistical reasons prevent you from having larger subgroups or when there is no reasonable basis for rational subgroups.

- Particularly useful when you are only making one observations per time period.

## XmR R Control Chart Definitions

**Range:** Based off of the consecutive differences in measures. First, find the average of your measurements. Then calculate the absolute

## How to Create & Use XmR Control Charts

- List all of your measurements
- Calculate the moving range by absolute difference between each measure by subtracting one from the other in sequential order.
- For example, if you have measures of 4, 6, 3, and 5, you will then get the following differences:
- (4-6) = 2
- 6-3 = 3
- (3-5) = 2

- For example, if you have measures of 4, 6, 3, and 5, you will then get the following differences:
- Calculate the mean of the samples.
- In our example the mean is 4 + 6+ 3 + 5 = 18. 18/4 = 4.5

- Calculate the mean of the individual moving ranges. This will act as the control limit – plot this horizontally on the graph.
- 2 + 3+ 2 = 7. 7/3 = 2.333

- Calculate the Upper & Lower Control Limits.
- UCL = Sample mean + 3* MR mean / d2
- LCL = Sample mean – 3* MR mean / d2
- d comes from a chart – you can find this in most reference books like this one.
- The 3 refers to 3 standard deviations.
- UCL in our example would =4.5 + (3 * 2.333 / d2)
- LCL in our example would =4.5 – (3 * 2.333 / d2)

- Plot upper control limits (ucl) and lower control limits (lcl)

## Examples of Uses of XmR Control Charts

## Important notes on XmR Control Charts

- Remember to NEVER put specifications on any kind of control chart.
- Use an X Bar S chart when the sample size is > 10.
- Use an X Bar R chart when the sample size is <10.
- Use an XmR chart when the sample size s 1.

## Comments (3)

Good Morning Sir/Madam,

First of all, thanks for the important & useful information provided here by you, with detailed explanations.

I have a query that, here in “X-mR Chart” information page, you mentioned “X Bar R” chart word throughout the page. I think, there may be some typographical mistake, i.e. ‘X Bar R’ instead of ‘X-mR’.

Please confirm and clarify my doubts, and do the required changes.

Thanking you in anticipation.

Thanks & Regards,

Prasad V. Dhawle

Absolutely correct, Prasad. I’ve updated. Thanks for pointing it out!

I want to underline a small remark:

In the case of an XmR chart the value 2.66 is obtained by dividing 3 by the sample size-specific d2 anti-biasing constant for n=2, as given in most textbooks on statistical process control.

what i mean it is useless to keep d2 as a variable. because in any event is always n = 2 what gives us d2 = 1.128

I insisted on this point because often we pose this confusion: as long as we have individual data why n = 2

Thank you the article is very clear.