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How are control limits calculated for an attribute u-chart?
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Last Updated
10th of November, 2010

A u-chart displays the number of nonconformities per unit produced.  This chart is available in WinSPC to an attribute that is configured with an 'Attribute Counts' of 'Defects' (also referred to as a 'Defect List').

An attribute displaying a u-chart in WinSPC (configured to recalculate the control limits every 5 subgroups) can be seen here:
samplenuchart.png

The statistic plotted on a u-chart chart is

uchartstatistic.png

where dk.png is the total number of non-conformities found in all the units in the lot, and nk.png is the lot size.


The following equations are used to calculate the control limits for the k-th subgroup:
attributeucluchartequation.png
attributecluchartequation.png
attributelcluchartequation.png


Where:
ubar.png is either
  • the sum of the total non-conformities divided by the sum of the lot sizes of a set of plotted values (taking into account the 'All Data', 'Last N subgroups', and 'Use local data only' options on the 'Control Limits' tab of the attribute properties), if the 'Est. based on process variables' option is selected under the 'Chart Statistic' area.  In other words, represented as an equation:
     ubar_def.png
  • or, the value entered for the 'Constant' option, if it is selected under the 'Chart Statistic' area.
nsigma.png is the 'Number of sigma' option under the 'Control Limit Spread' area on the 'Control Limits' tab of the attribute properties.  By default, this is 3.0.
nk.png is the lot size of the k-th subgroup.

If the calculation for LCL results in a value less than zero, the LCL is set to zero.

Note that the control limits will recalculate at the interval defined by the 'Calculated every k subgroups' option (25 by default).

For reference for the above control limit settings, here is a sample 'Control Limits' tab of the attribute properties:
attributepropertiesuchart.png




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