XbarR Chart Formulas

QI Macros can calculate them for you!

Create an XbarR Chart using QI Macros

Select your data.
Select the chart on QI Macros menu.
QI Macros will do the math and draw the graph for you.

Go Deeper:

The XbarR 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.

XbarR Chart formulas used in QI Macros add-in

Range Charts

x bar r range chart formulas

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

NOTE: It is possible to have negative limits on an XbarR Chart.

* "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.