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ProcessControl

 EWMAChart
 generate the EWMA chart
 • EWMAChart(X, options, plotoptions)

Parameters

 X - data options - (optional) equation(s) of the form option=value where option is one of color, confidencelevel, controllimits, ignore, lambda, mu, samplesize, or sigma; specify options for generating the EWMA chart plotoptions - (optional) parameters to pass to the plot command

Description

 • The EWMAChart command generates the exponentially weighted moving average (EWMA) control chart for the specified observations. The chart also contains the upper control limit (UCL), the lower control limit (LCL), and the mean value (represented by the center line) of the underlying quality characteristic. Unless explicitly given, the control limits are computed based on the data.
 • The first parameter X is a single data sample, given as a Vector or list. Each value represents the mean of an individual sample.

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.
 • color=list -- This option specifies colors of the various components of the EWMA chart. The value of this option must be a list containing the color of the control limits, center line, data to be plotted, and the specification limits.
 • confidencelevel=realcons -- This option specifies the required confidence level. The default value is 0.9973, corresponding to a 3 sigma confidence level.
 • controllimits=deduce or [realcons, realcons] -- This option specifies the values for the control limits. The first element is the value of the lower control limit. The second element is the value of the upper control limit. For data with variable sample size, the value of this option must be a list of control limits for each sample. If this option is set to deduce (the default value), the control limits are computed based on the data.
 • ignore=truefalse -- This option controls how missing values are handled by the EWMAChart command. Missing values are represented by undefined or Float(undefined). So, if ignore=false and X contains missing data, the EWMAChart 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

 > $\mathrm{with}\left(\mathrm{ProcessControl}\right):$
 > ${\mathrm{infolevel}}_{\mathrm{ProcessControl}}≔1:$
 > $A≔\left[10.5,6,10,11,12.5,9.5,6,10,10.5,14.5,9.5,12,12.5,10.5,8,9.5,7,10,13,9,12,6,12,15,11,7,9.5,10,12,8,9,13,11,9,10,15,12,8\right]:$
 > $\mathrm{EWMAChart}\left(A\right)$
 > $\mathrm{EWMAControlLimits}\left(A\right)$
 $\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)
 > $\mathrm{EWMAControlLimits}\left(A,\mathrm{λ}=0.5\right)$
 $\left[\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]{,}\left[{6.22929338151343}{,}{14.3496539869076}\right]\right]$ (2)
 > $\mathrm{EWMAControlLimits}\left(A,\mathrm{samplesize}=10\right)$
 $\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]$ (3)
 > $l≔\mathrm{EWMAControlLimits}\left(A,\mathrm{confidencelevel}=0.95\right)$
 ${l}{≔}\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]$ (4)
 > $\mathrm{EWMAChart}\left(A,\mathrm{controllimits}=l\right)$

References

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