Individuals-Control-Chart
Individuals-Control-Chart image from Smarter Solutions

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
  • 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.

IMR Video

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

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.

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