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ProcessControl

 UChart
 generate the U chart

 Calling Sequence UChart(X, n, options, plotoptions)

Parameters

 X - data n - sample size options - (optional) equation(s) of the form option=value where option is one of color, confidencelevel, controllimits, or ubar; specify options for generating the U chart plotoptions - (optional) parameters to pass to the plot command

Description

 • The UChart command generates the control chart for average number of nonconformities per inspection unit (U chart) for the specified observations. The chart also contains the upper control limit (UCL), the lower control limit (LCL), and the average number of nonconformities per inspection unit (represented by the center line) of the underlying quality characteristic. Unless explicitly given, the average number of nonconformities per unit and 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 number of nonconformities in the corresponding sample.
 • The second parameter n specifies the size of the samples. It can be either a positive integer, in which case all samples are assumed to be of size n, or a list (or Vector) of positive integers. Each value represents the size of the corresponding 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 U 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.
 • ubar=deduce or realcons -- This option specifies the average number of nonconformities per inspection unit.

Examples

 > $\mathrm{with}\left(\mathrm{ProcessControl}\right):$
 > $\mathrm{infolevel}\left[\mathrm{ProcessControl}\right]≔1:$
 > $A≔\left[12,8,6,9,10,12,11,16,10,6,20,15,9,8,6,8,10,7,5,8,5,8,10,6,9\right]$
 ${A}{≔}\left[{12}{,}{8}{,}{6}{,}{9}{,}{10}{,}{12}{,}{11}{,}{16}{,}{10}{,}{6}{,}{20}{,}{15}{,}{9}{,}{8}{,}{6}{,}{8}{,}{10}{,}{7}{,}{5}{,}{8}{,}{5}{,}{8}{,}{10}{,}{6}{,}{9}\right]$ (1)
 > $N≔\left[100,80,80,100,110,110,100,100,90,90,110,120,120,120,110,80,80,80,90,100,100,100,100,90,90\right]$
 ${N}{≔}\left[{100}{,}{80}{,}{80}{,}{100}{,}{110}{,}{110}{,}{100}{,}{100}{,}{90}{,}{90}{,}{110}{,}{120}{,}{120}{,}{120}{,}{110}{,}{80}{,}{80}{,}{80}{,}{90}{,}{100}{,}{100}{,}{100}{,}{100}{,}{90}{,}{90}\right]$ (2)

The command to create the plot from the Plotting Guide is

 > $\mathrm{UChart}\left(A,N\right)$
 > $\mathrm{UChart}\left(A,100\right)$
 Estimated Control Limits: [.00181764853697591, .185382351463024]
 > $\mathrm{UControlLimits}\left(A,N\right)$
 $\left[\left[{0.00279602820106184}{,}{0.188224379962204}\right]{,}\left[{0.}{,}{0.199167803958239}\right]{,}\left[{0.}{,}{0.199167803958239}\right]{,}\left[{0.00279602820106184}{,}{0.188224379962204}\right]{,}\left[{0.00711070588132663}{,}{0.183909702281939}\right]{,}\left[{0.00711070588132663}{,}{0.183909702281939}\right]{,}\left[{0.00279602820106184}{,}{0.188224379962204}\right]{,}\left[{0.00279602820106184}{,}{0.188224379962204}\right]{,}\left[{0.}{,}{0.193239526474135}\right]{,}\left[{0.}{,}{0.193239526474135}\right]{,}\left[{0.00711070588132663}{,}{0.183909702281939}\right]{,}\left[{0.0108741281902800}{,}{0.180146279972986}\right]{,}\left[{0.0108741281902800}{,}{0.180146279972986}\right]{,}\left[{0.0108741281902800}{,}{0.180146279972986}\right]{,}\left[{0.00711070588132663}{,}{0.183909702281939}\right]{,}\left[{0.}{,}{0.199167803958239}\right]{,}\left[{0.}{,}{0.199167803958239}\right]{,}\left[{0.}{,}{0.199167803958239}\right]{,}\left[{0.}{,}{0.193239526474135}\right]{,}\left[{0.00279602820106184}{,}{0.188224379962204}\right]{,}\left[{0.00279602820106184}{,}{0.188224379962204}\right]{,}\left[{0.00279602820106184}{,}{0.188224379962204}\right]{,}\left[{0.00279602820106184}{,}{0.188224379962204}\right]{,}\left[{0.}{,}{0.193239526474135}\right]{,}\left[{0.}{,}{0.193239526474135}\right]\right]$ (3)
 > $l≔\mathrm{UControlLimits}\left(A,N,\mathrm{confidencelevel}=0.90\right)$
 ${l}{≔}\left[\left[{0.0446764547135566}{,}{0.146343953449709}\right]{,}\left[{0.0386763445107801}{,}{0.152344063652485}\right]{,}\left[{0.0386763445107801}{,}{0.152344063652485}\right]{,}\left[{0.0446764547135566}{,}{0.146343953449709}\right]{,}\left[{0.0470421257850995}{,}{0.143978282378166}\right]{,}\left[{0.0470421257850995}{,}{0.143978282378166}\right]{,}\left[{0.0446764547135566}{,}{0.146343953449709}\right]{,}\left[{0.0446764547135566}{,}{0.146343953449709}\right]{,}\left[{0.0419267274101495}{,}{0.149093680753116}\right]{,}\left[{0.0419267274101495}{,}{0.149093680753116}\right]{,}\left[{0.0470421257850995}{,}{0.143978282378166}\right]{,}\left[{0.0491055520584020}{,}{0.141914856104863}\right]{,}\left[{0.0491055520584020}{,}{0.141914856104863}\right]{,}\left[{0.0491055520584020}{,}{0.141914856104863}\right]{,}\left[{0.0470421257850995}{,}{0.143978282378166}\right]{,}\left[{0.0386763445107801}{,}{0.152344063652485}\right]{,}\left[{0.0386763445107801}{,}{0.152344063652485}\right]{,}\left[{0.0386763445107801}{,}{0.152344063652485}\right]{,}\left[{0.0419267274101495}{,}{0.149093680753116}\right]{,}\left[{0.0446764547135566}{,}{0.146343953449709}\right]{,}\left[{0.0446764547135566}{,}{0.146343953449709}\right]{,}\left[{0.0446764547135566}{,}{0.146343953449709}\right]{,}\left[{0.0446764547135566}{,}{0.146343953449709}\right]{,}\left[{0.0419267274101495}{,}{0.149093680753116}\right]{,}\left[{0.0419267274101495}{,}{0.149093680753116}\right]\right]$ (4)
 > $\mathrm{UChart}\left(A,N,\mathrm{controllimits}=l\right)$

References

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