UControlLimits - Maple Help
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ProcessControl

 UControlLimits
 compute control limits for the U chart

 Calling Sequence UControlLimits(X, n, options)

Parameters

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

Description

 • The UControlLimits command computes the upper and lower control limits for the U chart. Unless explicitly given, the standard deviation of the underlying quality characteristic is 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.
 • 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.
 • ubar=deduce or realcons -- This option specifies the average number of nonconformities per inspection unit.

Examples

 > $\mathrm{with}\left(\mathrm{ProcessControl}\right):$
 > ${\mathrm{infolevel}}_{\mathrm{ProcessControl}}≔1:$
 > $A≔\left[12,8,6,9,10,12,11,16,10,6,20,15,9,8,6,8,10,7,5,8,5,8,10,6,9\right]$
 ${A}{≔}\left[{12}{,}{8}{,}{6}{,}{9}{,}{10}{,}{12}{,}{11}{,}{16}{,}{10}{,}{6}{,}{20}{,}{15}{,}{9}{,}{8}{,}{6}{,}{8}{,}{10}{,}{7}{,}{5}{,}{8}{,}{5}{,}{8}{,}{10}{,}{6}{,}{9}\right]$ (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)
 > $\mathrm{UControlLimits}\left(A,N\right)$
 $\left[\left[{0.00279602820627355}{,}{0.188224379956992}\right]{,}\left[{0.}{,}{0.199167803949220}\right]{,}\left[{0.}{,}{0.199167803958239}\right]{,}\left[{0.00279602820106184}{,}{0.188224379962204}\right]{,}\left[{0.00711070589174154}{,}{0.183909702271524}\right]{,}\left[{0.00711070588132663}{,}{0.183909702281939}\right]{,}\left[{0.00279602820106184}{,}{0.188224379962204}\right]{,}\left[{0.00279602820106184}{,}{0.188224379962204}\right]{,}\left[{0.}{,}{0.193239526465490}\right]{,}\left[{0.}{,}{0.193239526474135}\right]{,}\left[{0.00711070588132663}{,}{0.183909702281939}\right]{,}\left[{0.0108741282025735}{,}{0.180146279960692}\right]{,}\left[{0.0108741281902800}{,}{0.180146279972986}\right]{,}\left[{0.0108741281902800}{,}{0.180146279972986}\right]{,}\left[{0.00711070588132663}{,}{0.183909702281939}\right]{,}\left[{0.}{,}{0.199167803958239}\right]{,}\left[{0.}{,}{0.199167803958239}\right]{,}\left[{0.}{,}{0.199167803958239}\right]{,}\left[{0.}{,}{0.193239526474135}\right]{,}\left[{0.00279602820106184}{,}{0.188224379962204}\right]{,}\left[{0.00279602820106184}{,}{0.188224379962204}\right]{,}\left[{0.00279602820106184}{,}{0.188224379962204}\right]{,}\left[{0.00279602820106184}{,}{0.188224379962204}\right]{,}\left[{0.}{,}{0.193239526474135}\right]{,}\left[{0.}{,}{0.193239526474135}\right]\right]$ (3)
 > $\mathrm{UControlLimits}\left(A,N,\mathrm{confidencelevel}=0.95\right)$
 $\left[\left[{0.0349380556983448}{,}{0.156082352464920}\right]{,}\left[{0.0277884834154296}{,}{0.163231924747836}\right]{,}\left[{0.0277884834154296}{,}{0.163231924747836}\right]{,}\left[{0.0349380556983448}{,}{0.156082352464920}\right]{,}\left[{0.0377569266443770}{,}{0.153263481518888}\right]{,}\left[{0.0377569266443770}{,}{0.153263481518888}\right]{,}\left[{0.0349380556983448}{,}{0.156082352464920}\right]{,}\left[{0.0349380556983448}{,}{0.156082352464920}\right]{,}\left[{0.0316615535259485}{,}{0.159358854637317}\right]{,}\left[{0.0316615535259485}{,}{0.159358854637317}\right]{,}\left[{0.0377569266443770}{,}{0.153263481518888}\right]{,}\left[{0.0402156506999146}{,}{0.150804757463351}\right]{,}\left[{0.0402156506999146}{,}{0.150804757463351}\right]{,}\left[{0.0402156506999146}{,}{0.150804757463351}\right]{,}\left[{0.0377569266443770}{,}{0.153263481518888}\right]{,}\left[{0.0277884834154296}{,}{0.163231924747836}\right]{,}\left[{0.0277884834154296}{,}{0.163231924747836}\right]{,}\left[{0.0277884834154296}{,}{0.163231924747836}\right]{,}\left[{0.0316615535259485}{,}{0.159358854637317}\right]{,}\left[{0.0349380556983448}{,}{0.156082352464920}\right]{,}\left[{0.0349380556983448}{,}{0.156082352464920}\right]{,}\left[{0.0349380556983448}{,}{0.156082352464920}\right]{,}\left[{0.0349380556983448}{,}{0.156082352464920}\right]{,}\left[{0.0316615535259485}{,}{0.159358854637317}\right]{,}\left[{0.0316615535259485}{,}{0.159358854637317}\right]\right]$ (4)
 > $\mathrm{UControlLimits}\left(A,100\right)$
 $\left[{0.00181764853697591}{,}{0.185382351463024}\right]$ (5)
 > $\mathrm{UControlLimits}\left(A,100,\mathrm{confidencelevel}=0.95\right)$
 $\left[{0.0336366323844170}{,}{0.153563367615583}\right]$ (6)

References

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

 See Also