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ProcessControl

 EWMAControlLimits
 compute control limits for the EWMA chart

 Calling Sequence EWMAControlLimits(X, options)

Parameters

 X - data options - (optional) equation(s) of the form option=value where option is one of confidencelevel, ignore, lambda, mu, samplesize, or sigma; specify options for computing the control limits

Description

 • The EWMAControlLimits command computes the upper and lower control limits for the EWMA chart. Unless explicitly given, the mean and the standard deviation of the underlying quality characteristic are computed based on the data.
 • The first parameter X is either a single data sample - given as a Vector or list - or a list of data samples. Each value represents an individual observation. Note, that the individual samples can be of variable size.
 • If X is a single data sample, the second parameter n is used to specify the size of individual samples.

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.

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 EWMAControlLimits command. Missing values are represented by undefined or Float(undefined). So, if ignore=false and X contains missing data, the EWMAControlLimits command returns undefined. If ignore=true, all missing items in X are ignored. The default value is true.
 • lambda=realcons -- This option specifies the value of the smoothing parameter. The default value is 0.2.
 • mu=deduce or realcons -- This option specifies the mean of the underlying quality characteristic.
 • samplesize=posint -- This option specifies the size of individual samples. The default value is 1.
 • sigma=deduce or realcons -- This option specifies the standard deviation of the underlying quality characteristic.

Examples

 > $\mathrm{with}\left(\mathrm{ProcessControl}\right):$
 > ${\mathrm{infolevel}}_{\mathrm{ProcessControl}}≔1:$
 > $A≔\left[10.5,6,10,11,12.5,9.5,6,10,10.5,14.5,9.5,12,12.5,10.5,8,9.5,7,10,13,9,12,6,12,15,11,7,9.5,10,12,8,9,13,11,9,10,15,12,8\right]:$
 > $\mathrm{EWMAControlLimits}\left(A\right)$
 $\left[\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]{,}\left[{7.94532749376648}{,}{12.6336198746546}\right]\right]$ (1)
 > $\mathrm{EWMAControlLimits}\left(A,\mathrm{samplesize}=10\right)$
 $\left[\left[{9.84470321651778}{,}{10.7342441519033}\right]{,}\left[{9.71988957184900}{,}{10.8590577965721}\right]{,}\left[{9.65272141838936}{,}{10.9262259500317}\right]{,}\left[{9.61322596653524}{,}{10.9657214018858}\right]{,}\left[{9.58911677992714}{,}{10.9898305884939}\right]{,}\left[{9.57411319000254}{,}{11.0048341784185}\right]{,}\left[{9.56467386602539}{,}{11.0142735023957}\right]{,}\left[{9.55869668281095}{,}{11.0202506856101}\right]{,}\left[{9.55489680907764}{,}{11.0240505593434}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]{,}\left[{9.54818957138928}{,}{11.0307577970318}\right]\right]$ (2)
 > $\mathrm{EWMAControlLimits}\left(A,\mathrm{confidencelevel}=0.95\right)$
 $\left[\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]{,}\left[{8.75799298526542}{,}{11.8209543831556}\right]\right]$ (3)

References

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