X bar R Chart Formulas

The X bar R chart can help you evaluate the stability of processes using variable data--time, cost, length, weight when you have 2 to 10 samples per period.

Here are the X bar R chart formulas used in QI Macros for both the Range and Average (Xbar) charts:

Range Charts

Average (Xbar) Chart

xbar chart formula

k = number of subgroups (a group of measurements produced under the same set of conditions)

n = number of samples in a subgroup

A₂, D₃ and D₄ are constants based on n

Conforms with ANSI/ASQC B1, B2, B3 1996

* "Introduction to Statistical Quality Control," Douglas C. Montgomery *

Process: Calculate, plot, and evaluate the range chart first. If it is "out of control," so is the process. If the range chart looks okay, then calculate, plot, and evaluate the X chart.

Note: Some people wonder why QI Macros results are a tiny bit different from some versions of other software. The answer is that they use a different estimator. Donald Wheeler in Advanced Topics in Statistical Process Control says: "Even though the Pooled [Standard Deviation] estimator is common in many applications, the robustness of Rbar/d2 and Sbar/c4 makes them the preferred estimators for use with process behavior charts."

Furthermore, Minitab started using Pooled Standard Deviation to calculate Cp/Cpk, and control limits on XbarR and XbarS charts in versions 15 and 16. Minitab 17 went back to Rbar/d2 and Sbar/c4 for XbarR/S control limits, but retained pooled stdev for Cp/Cpk calculations when using multiple samples.