Sigma Chart Calculations

Plotted statistic

The subgroup standard deviation

where xi are the observations in subgroup j, x-barj is the subgroup average for subgroup j, and n is the subgroup size.

Center Line

Average Sigma

UCL , LCL (Upper and Lower Control Limit)

where S-bar is the Average Sigma , c4 is a function of n .

Notes: Some authors prefer to write this as:

where B3 and B4 are a function of n (available in any statistical quality control textbook).

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).