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.

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.

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.

$\mathrm{with}\left(\mathrm{ProcessControl}\right)\:$

$\mathrm{infolevel}\left[\mathrm{ProcessControl}\right]≔1\:$

$A≔\left[12\,8\,6\,9\,10\,12\,11\,16\,10\,6\,20\,15\,9\,8\,6\,8\,10\,7\,5\,8\,5\,8\,10\,6\,9\right]$

$A≔\left[12\,8\,6\,9\,10\,12\,11\,16\,10\,6\,20\,15\,9\,8\,6\,8\,10\,7\,5\,8\,5\,8\,10\,6\,9\right]$

$N≔\left[100\,80\,80\,100\,110\,110\,100\,100\,90\,90\,110\,120\,120\,120\,110\,80\,80\,80\,90\,100\,100\,100\,100\,90\,90\right]$

$N≔\left[100\,80\,80\,100\,110\,110\,100\,100\,90\,90\,110\,120\,120\,120\,110\,80\,80\,80\,90\,100\,100\,100\,100\,90\,90\right]$

$\mathrm{UControlLimits}\left(A\,N\right)$

$\left[\left[0.00279602820627355\,0.188224379956992\right]\,\left[0.\,0.199167803949220\right]\,\left[0.\,0.199167803958239\right]\,\left[0.00279602820106184\,0.188224379962204\right]\,\left[0.00711070589174154\,0.183909702271524\right]\,\left[0.00711070588132663\,0.183909702281939\right]\,\left[0.00279602820106184\,0.188224379962204\right]\,\left[0.00279602820106184\,0.188224379962204\right]\,\left[0.\,0.193239526465490\right]\,\left[0.\,0.193239526474135\right]\,\left[0.00711070588132663\,0.183909702281939\right]\,\left[0.0108741282025735\,0.180146279960692\right]\,\left[0.0108741281902800\,0.180146279972986\right]\,\left[0.0108741281902800\,0.180146279972986\right]\,\left[0.00711070588132663\,0.183909702281939\right]\,\left[0.\,0.199167803958239\right]\,\left[0.\,0.199167803958239\right]\,\left[0.\,0.199167803958239\right]\,\left[0.\,0.193239526474135\right]\,\left[0.00279602820106184\,0.188224379962204\right]\,\left[0.00279602820106184\,0.188224379962204\right]\,\left[0.00279602820106184\,0.188224379962204\right]\,\left[0.00279602820106184\,0.188224379962204\right]\,\left[0.\,0.193239526474135\right]\,\left[0.\,0.193239526474135\right]\right]$

$\mathrm{UControlLimits}\left(A\,N\,\mathrm{confidencelevel}=0.95\right)$

$\left[\left[0.0349380556983448\,0.156082352464920\right]\,\left[0.0277884834154296\,0.163231924747836\right]\,\left[0.0277884834154296\,0.163231924747836\right]\,\left[0.0349380556983448\,0.156082352464920\right]\,\left[0.0377569266443770\,0.153263481518888\right]\,\left[0.0377569266443770\,0.153263481518888\right]\,\left[0.0349380556983448\,0.156082352464920\right]\,\left[0.0349380556983448\,0.156082352464920\right]\,\left[0.0316615535259485\,0.159358854637317\right]\,\left[0.0316615535259485\,0.159358854637317\right]\,\left[0.0377569266443770\,0.153263481518888\right]\,\left[0.0402156506999146\,0.150804757463351\right]\,\left[0.0402156506999146\,0.150804757463351\right]\,\left[0.0402156506999146\,0.150804757463351\right]\,\left[0.0377569266443770\,0.153263481518888\right]\,\left[0.0277884834154296\,0.163231924747836\right]\,\left[0.0277884834154296\,0.163231924747836\right]\,\left[0.0277884834154296\,0.163231924747836\right]\,\left[0.0316615535259485\,0.159358854637317\right]\,\left[0.0349380556983448\,0.156082352464920\right]\,\left[0.0349380556983448\,0.156082352464920\right]\,\left[0.0349380556983448\,0.156082352464920\right]\,\left[0.0349380556983448\,0.156082352464920\right]\,\left[0.0316615535259485\,0.159358854637317\right]\,\left[0.0316615535259485\,0.159358854637317\right]\right]$

$\mathrm{UControlLimits}\left(A\,100\right)$

$\left[0.00181764853697591\,0.185382351463024\right]$

$\mathrm{UControlLimits}\left(A\,100\,\mathrm{confidencelevel}=0.95\right)$

$\left[0.0336366323844170\,0.153563367615583\right]$

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