Prediction Error Sigma

The smoothed standard deviation of the prediction errors.

 for t≥1

where

 is the Error Weighting Factor (user defined)

the one step ahead prediction error, et, is the calculated difference between the observation and the forecast

the starting value of λ is calculated (for m observations) as:.

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).