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ProcessControl

  

UControlLimits

  

compute control limits for the U chart

 

Calling Sequence

Parameters

Description

Computation

Options

Examples

References

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

withProcessControl:

infolevelProcessControl1:

A12,8,6,9,10,12,11,16,10,6,20,15,9,8,6,8,10,7,5,8,5,8,10,6,9

A:=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

(1)

N100,80,80,100,110,110,100,100,90,90,110,120,120,120,110,80,80,80,90,100,100,100,100,90,90

N:=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

(2)

UControlLimitsA,N

0.00279602820627355,0.188224379956992,0.,0.199167803949220,0.,0.199167803958239,0.00279602820106184,0.188224379962204,0.00711070589174154,0.183909702271524,0.00711070588132663,0.183909702281939,0.00279602820106184,0.188224379962204,0.00279602820106184,0.188224379962204,0.,0.193239526465490,0.,0.193239526474135,0.00711070588132663,0.183909702281939,0.0108741282025735,0.180146279960692,0.0108741281902800,0.180146279972986,0.0108741281902800,0.180146279972986,0.00711070588132663,0.183909702281939,0.,0.199167803958239,0.,0.199167803958239,0.,0.199167803958239,0.,0.193239526474135,0.00279602820106184,0.188224379962204,0.00279602820106184,0.188224379962204,0.00279602820106184,0.188224379962204,0.00279602820106184,0.188224379962204,0.,0.193239526474135,0.,0.193239526474135

(3)

UControlLimitsA,N,confidencelevel=0.95

0.0349380557017498,0.156082352461516,0.0277884834213217,0.163231924741944,0.0277884834154296,0.163231924747836,0.0349380556983448,0.156082352464920,0.0377569266511813,0.153263481512084,0.0377569266443770,0.153263481518888,0.0349380556983448,0.156082352464920,0.0349380556983448,0.156082352464920,0.0316615535315967,0.159358854631669,0.0316615535259485,0.159358854637317,0.0377569266443770,0.153263481518888,0.0402156507079462,0.150804757455319,0.0402156506999146,0.150804757463351,0.0402156506999146,0.150804757463351,0.0377569266443770,0.153263481518888,0.0277884834154296,0.163231924747836,0.0277884834154296,0.163231924747836,0.0277884834154296,0.163231924747836,0.0316615535259485,0.159358854637317,0.0349380556983448,0.156082352464920,0.0349380556983448,0.156082352464920,0.0349380556983448,0.156082352464920,0.0349380556983448,0.156082352464920,0.0316615535259485,0.159358854637317,0.0316615535259485,0.159358854637317

(4)

UControlLimitsA,100

0.00181764853697591,0.185382351463024

(5)

UControlLimitsA,100,confidencelevel=0.95

0.0336366323844170,0.153563367615583

(6)

References

  

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

See Also

infolevel

ProcessControl

ProcessControl[UChart]

Statistics

 


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