X Bar R Control Charts

X Bar R Chart
X Bar R Chart

X Bar R Chart image from Minitab

An X-bar, R chart is actually 2 plots between the process mean and the process range over time and is an example of statistical process control. This combination helps you understand the stability of processes detect the presence of special cause variation.

Use X Bar R Control Charts When:

  • When you can rationally collect measurements in subgroups of generally between two and 10 observations.
  • Small amounts of constant, continuous data
    • In other words, the sample sizes must be constant.
  • The measurements are at regular intervals.
  • We can assume the data is normally distributed.
  • The sampling procedure is same for each sample and is carried out consistently.

X Bar R Control Chart Definitions

R-chart: the range from subgroups values. This monitors the process standard deviation (as approximated by the sample moving range)

X-bar chart:the average from subgroup values. The control limits on the X-Bar brings the sample’s spread and center into consideration.

How to Use X Bar R Control Charts

  • Check the R chart for control.
  • If not in control, stop.
    • If the R chart is out of control, then the control limits on the Xbar chart may be inaccurate and ruin any other analysis.
  • If in control, check the Xbar chart.
    •  Only valid if the within-sample variability is constant (that’s why we check the R chart first.)

Examples of Uses of X Bar R Control Charts

  • Monitoring the process mean and variation for subgroups of
    • Production processes.
      • Ex. Part lengths.
    • Call handle times.
    • Hospital patients’ blood pressure over time.
    • Agile software development MMF development times.

Important notes on X Bar R Control Charts

  • Remember to NEVER put specifications on any kind of control chart.
  • The operator might have the tendency to not react to a point out control when the point is within the specification limits.
  • The points on the chart are comprised of averages, not individuals. Specification limits are based on individuals, not averages.
  • You want most of the points to be out of control on the x-bar portion because the dots show you the product variation; whereas the more narrow (ideally) width of the control limits reveals the slop in the measurement system.
  • You want the slop in the measurement system to be less than the variation in the product.



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