Individuals-Control-Chart image from Smarter Solutions

An XmR chart (aka Shewhart’s Control Chart) calculates the control limits from the moving average range.

When to Use XmR Control Charts:

  • When you have continuous data.
  • When you have subgroups of size = 1.
    • You use the 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 observation per time period.

XmR R Control Chart Definitions

Range: Based on the consecutive differences in measures. First, find the average of your measurements, then calculate the absolute difference.

How to Create & Use XmR Control Charts

  • List all of your measurements for your XmR control chart.
  • Calculate the moving range by using the absolute difference between each measure and subtracting one from the other sequentially.
    • 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 for the XmR control chart
    • 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)

Important notes

  • Remember to NEVER put specifications on any kind of control chart, including the XmR chart.
  • Use an X Bar S chart when the subgroup size is > 10.
  • Use an X Bar R chart when the subgroup size is between 2 & 10.
  • Use an XmR chart when the sample size is 1 && there is a lot of data.
  • Use an ImR chart when the subgroup size is 1 && there is NOT a lot of data.


Comments (8)

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.

Hi.. I have a question about XnR charts and SPC in general. It is my understanding that this was designed for manufacturing but can these be leveraged to monitor human-driven workflows (e.g. HR Procurement) vs manufacturing industry?

I have been trying to find articles on this but thus far no luck. Yet, it feels like it should work especially since in the case of HR procurement workflows data we are dealing with we have the entire population of the data.

Any thoughts anyone?

You are dividing by 3 because , the numerator is sum of the 3 values (2 + 3+ 2 ) . For Sample Mean , you are dividing by 4 because , the numerator is a sum of 4 values ( 4 + 6+ 3 + 5) .Hope this clarifies.
**Posting this because it may be useful for somehow who gets similar query**

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