XmR Charts (Shewhart’s Control Chart, ImR Chart)

Individuals-Control-Chart
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 X Bar R 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.

 

X Bar 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 X Bar R 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 X Bar R Control Charts

Important notes on X Bar R 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.
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