X Bar Chart Calculations

Plotted statistic

Subgroup Average

Center Line

Grand Average

UCL , LCL (Upper and Lower Control Limit)

where x-double bar is the Grand Average and σx is Process Sigma, which is calculated using the Subgroup Range or Subgroup Sigma statistic.

Notes: Some authors prefer to write this x-bar chart formula as:

where R-bar is the Average Range , or

where S-bar is the Average Sigma .

Learn more about the SPC principles and tools for process improvement in Statistical Process Control Demystified (2011, McGraw-Hill) by Paul Keller, in his online SPC Concepts short course (only $39), or his online SPC certification course ($350) or online Green Belt certification course ($499).