Standardized Observations

Observations, for use on any variables control chart, can be standardized for use in Short Run Processes as follows:

For use as Nominal Control Charts:

$images\conc0121_wmf.jpg$

where xi is the observation and Nominal is a constant, based on prior data or a desired value.

For use as Stabilized Control Charts:

Dispersion entered as range (if the variation estimate is a Range estimate):

$images\conc0122_wmf.jpg$ (When Range chart used)

$images\conc0123_wmf.jpg$ (When Sigma chart used)

where xi is the observation, Nominal and Range are the constants used for standardizing that run, d2 and c4 are a function of the subgroup size (moving size for Moving Average charts).

Dispersion entered as sample sigma: (if the variation estimate is a Sample Sigma estimate):

$images\conc0124_wmf.jpg$ (When Range chart used)

$images\conc0125_wmf.jpg$ (When Sigma chart used)

where xi is the observation, Nominal and Sample Sigma are the constants used for standardizing that run, d2 and c4 are a function of the subgroup size (moving size for Moving Average charts)..

Dispersion entered as process sigma: (if the variation estimate is a Process Sigma estimate):

$images\conc0126_wmf.jpg$ (When Range chart used)

$images\conc0127_wmf.jpg$ (When Sigma chart used)

where xi is the observation, Nominal and Process Sigma are the constants used for standardizing that run, d2 and c4 are a function of the subgroup size (moving size for Moving Average charts).

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).