The XControlLimits command computes the upper and lower control limits for the X chart. Unless explicitly given, the mean and the average of the moving ranges of two observations of the underlying quality characteristic are computed based on the data.

The first parameter X is a single data sample, given as a Vector or list. Each value represents an individual observation.

All computations involving data are performed in floating-point; therefore, all data provided must have type realcons and all returned solutions are floating-point, even if the problem is specified with exact values.

For more information about computation in the ProcessControl package, see the ProcessControl help page.

The options argument can contain one or more of the following options.

confidencelevel=realcons -- This option specifies the required confidence level. The default value is 0.9973, corresponding to a 3 sigma confidence level.

ignore=truefalse -- This option controls how missing values are handled by the XControlLimits command. Missing values are represented by undefined or Float(undefined). So, if ignore=false and X contains missing data, the XControlLimits command returns undefined. If ignore=true, all missing items in X are ignored. The default value is true.

rbar=deduce or realcons -- This option specifies the average of the moving ranges of two observations.

xbar=deduce or realcons -- This option specifies the mean value of the underlying quality characteristic.

$\mathrm{with}\left(\mathrm{ProcessControl}\right)\:$

$\mathrm{infolevel}\left[\mathrm{ProcessControl}\right]≔1\:$

$A≔\left[33.75\,33.05\,34.00\,33.81\,33.46\,34.02\,33.68\,33.27\,33.49\,33.20\,33.62\,33.00\,33.54\,33.12\,33.84\right]\:$

$\mathrm{XControlLimits}\left(A\right)$

$\left[32.2448378926038\,34.8018287740628\right]$

$l≔\mathrm{XControlLimits}\left(A\,\mathrm{confidencelevel}=0.95\right)$

$l≔\left[32.2448378926038\,34.8018287740628\right]$

Montgomery, Douglas C. Introduction to Statistical Quality Control. 2nd ed. New York: John Wiley & Sons, 1991.