Individual X Chart Calculations

Plotted statistic

The observation

Center Line

the Average (Normal Distribution)

the Median of the Fitted Distribution (Non-Normal Distributions)

UCL , LCL (Upper and Lower Control Limit)

The upper control limit for the observations selected for analysis.

UCLx = + 3σx  (Normal Distribution)

LCLx = - 3σx  (Normal Distribution)

where x-bar is the average and sigma-x is the process sigma .

Notes:

1. Some authors prefer to write this as:

UCLx = + 2.66

UCLx = - 2.66

1. For Non-Normal distributions, the UCLx is set to the percentile of the fitted distribution corresponding to the ordinate value for the Normal distribution. For example, the UCL for 3-sigma limits is defined at the 99.865 percentile of the fitted curve, and the LCL is defined at the 0.135 percentile of the fitted curve.

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).