How to Calculate Control Limits for Xbar-R and Xbar-S Control Charts in SPC Analysis and When to Use Each Chart

You may have noticed that when using Minitab to create Xbar-R and Xbar-S control charts, each is composed of a pair of charts:

• Xbar-R Control Chart includes: Xbar Control Chart and R Control Chart

• Xbar-S Control Chart includes: Xbar Control Chart and S Control Chart

So the questions arise:

1. For the same data source, are the Xbar Control Charts in the Xbar-R and Xbar-S Control Charts the same?
2. When should we use the Xbar-R Control Chart, and when should we use the Xbar-S Control Chart?
3. How are the control limits of these control charts calculated?

This article provides the most detailed explanation available on the internet.

To clarify, the Xbar Control Charts in the Xbar-R and Xbar-S Control Charts are not the same. The use of Xbar-R Control Chart and Xbar-S Control Chart is conditional; we should not use Xbar-R and Xbar-S simultaneously on the same set of inspection data. Therefore, we do not need to worry about whether the Xbar Control Charts in Xbar-R and Xbar-S are the same, because we will not be using Xbar-R and Xbar-S at the same time.

For subgroup sizes ≤10

we need to use the Xbar-R Control Chart. The control limits for the Xbar Control Chart and R Control Chart are calculated as follows:

• Rbar: The average of the ranges of each subgroup

For subgroup sizes >10

we need to use the Xbar-S Control Chart. The control limits for the Xbar Control Chart and S Control Chart are calculated as follows:

• Sbar: The average of the standard deviations of each subgroup (Note: The standard deviation should be calculated with the denominator $n-1$)

The SPC constants such as A2, D4, A3, B4, etc., used in these formulas are as follows: