PControlLimits - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

# Online Help

###### All Products    Maple    MapleSim

ProcessControl

 PControlLimits
 compute control limits for the P chart

 Calling Sequence PControlLimits(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 pbar; specify options for computing the control limits

Description

 • The PControlLimits command computes the upper and lower control limits for the P 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 nonconforming items 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.
 • pbar=deduce or realcons -- This option specifies the average fraction of nonconforming items per data sample.

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)
 > $\mathrm{PControlLimits}\left(A,N\right)$
 $\left[\left[{0.00733469451799994}{,}{0.183685713645266}\right]{,}\left[{0.}{,}{0.194093420749116}\right]{,}\left[{0.}{,}{0.194093420736166}\right]{,}\left[{0.00733469452185952}{,}{0.183685713641406}\right]{,}\left[{0.0114381544250419}{,}{0.179582253738224}\right]{,}\left[{0.0114381544116218}{,}{0.179582253751644}\right]{,}\left[{0.00733469452185952}{,}{0.183685713641406}\right]{,}\left[{0.00733469452185952}{,}{0.183685713641406}\right]{,}\left[{0.00256505605928631}{,}{0.188455352103979}\right]{,}\left[{0.00256505607051234}{,}{0.188455352092753}\right]{,}\left[{0.0114381544116218}{,}{0.179582253751644}\right]{,}\left[{0.0150173447357757}{,}{0.176003063427490}\right]{,}\left[{0.0150173447401369}{,}{0.176003063423129}\right]{,}\left[{0.0150173447401369}{,}{0.176003063423129}\right]{,}\left[{0.0114381544116218}{,}{0.179582253751644}\right]{,}\left[{0.}{,}{0.194093420736166}\right]{,}\left[{0.}{,}{0.194093420736166}\right]{,}\left[{0.}{,}{0.194093420736166}\right]{,}\left[{0.00256505607051234}{,}{0.188455352092753}\right]{,}\left[{0.00733469452185952}{,}{0.183685713641406}\right]{,}\left[{0.00733469452185952}{,}{0.183685713641406}\right]{,}\left[{0.00733469452185952}{,}{0.183685713641406}\right]{,}\left[{0.00733469452185952}{,}{0.183685713641406}\right]{,}\left[{0.00256505607051234}{,}{0.188455352092753}\right]{,}\left[{0.00256505607051234}{,}{0.188455352092753}\right]\right]$ (3)
 > $\mathrm{PControlLimits}\left(A,N,\mathrm{confidencelevel}=0.95\right)$
 $\left[\left[{0.0379032632001590}{,}{0.153117144963106}\right]{,}\left[{0.0311036861938802}{,}{0.159916721969385}\right]{,}\left[{0.0311036861938802}{,}{0.159916721969385}\right]{,}\left[{0.0379032632001590}{,}{0.153117144963106}\right]{,}\left[{0.0405841410590932}{,}{0.150436267104172}\right]{,}\left[{0.0405841410590932}{,}{0.150436267104172}\right]{,}\left[{0.0379032632001590}{,}{0.153117144963106}\right]{,}\left[{0.0379032632001590}{,}{0.153117144963106}\right]{,}\left[{0.0347871566796007}{,}{0.156233251483665}\right]{,}\left[{0.0347871566796007}{,}{0.156233251483665}\right]{,}\left[{0.0405841410590932}{,}{0.150436267104172}\right]{,}\left[{0.0429225024327639}{,}{0.148097905730501}\right]{,}\left[{0.0429225024327639}{,}{0.148097905730501}\right]{,}\left[{0.0429225024327639}{,}{0.148097905730501}\right]{,}\left[{0.0405841410590932}{,}{0.150436267104172}\right]{,}\left[{0.0311036861938802}{,}{0.159916721969385}\right]{,}\left[{0.0311036861938802}{,}{0.159916721969385}\right]{,}\left[{0.0311036861938802}{,}{0.159916721969385}\right]{,}\left[{0.0347871566796007}{,}{0.156233251483665}\right]{,}\left[{0.0379032632001590}{,}{0.153117144963106}\right]{,}\left[{0.0379032632001590}{,}{0.153117144963106}\right]{,}\left[{0.0379032632001590}{,}{0.153117144963106}\right]{,}\left[{0.0379032632001590}{,}{0.153117144963106}\right]{,}\left[{0.0347871566796007}{,}{0.156233251483665}\right]{,}\left[{0.0347871566796007}{,}{0.156233251483665}\right]\right]$ (4)
 > $\mathrm{PControlLimits}\left(A,100\right)$
 $\left[{0.00621857384815468}{,}{0.180981426151846}\right]$ (5)
 > $\mathrm{PControlLimits}\left(A,100,\mathrm{confidencelevel}=0.95\right)$
 $\left[{0.0365118507466331}{,}{0.150688149253367}\right]$ (6)

References

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

 See Also