XControlLimits - Maple Help
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ProcessControl

 XControlLimits
 compute control limits for the X chart

 Calling Sequence XControlLimits(X, n, options)

Parameters

 X - data n - (optional) sample size options - (optional) equation(s) of the form option=value where option is one of confidencelevel, ignore, rbar, or xbar; specify options for computing the control limits

Description

 • 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.

Computation

 • 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.

Options

 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.

Examples

 > $\mathrm{with}\left(\mathrm{ProcessControl}\right):$
 > ${\mathrm{infolevel}}_{\mathrm{ProcessControl}}≔1:$
 > $A≔\left[33.75,33.05,34.00,33.81,33.46,34.02,33.68,33.27,33.49,33.20,33.62,33.00,33.54,33.12,33.84\right]:$
 > $\mathrm{XControlLimits}\left(A\right)$
 $\left[{32.2448378926038}{,}{34.8018287740628}\right]$ (1)
 > $l≔\mathrm{XControlLimits}\left(A,\mathrm{confidencelevel}=0.95\right)$
 ${l}{≔}\left[{32.2448378926038}{,}{34.8018287740628}\right]$ (2)

References

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