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 Cpk and Cp with a Single Specification Limit

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Bill Rokos Posted - 29 Jul 2014 : 17:09:54
Hello,

My user has stated that they sometimes do not have a Upper Specification Limit. Is it possible to calculate this in the SPC Chart? If so, how is Cp or Pp calculated as I don't know how this would be possible?

I have found some internet sites that talk about single Specification Limits, but I am not sure this can be applied in the SPC Chart.

http://www.pqsystems.com/qualityadvisor/DataAnalysisTools/capability_indices_with_one_specification.php

http://www.isixsigma.com/topic/one-sided-tolerance-cpk/

Best Regards and Thanks for any help you can provide.
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quinncurtis Posted - 31 Jul 2014 : 13:31:23
Both of your references refer to Cpk, so I thought you were asking about Cpk rather than Cp. You are correct, in that there is no way to calculate the Cp value without both spec limits. However, Cpl and Cpu are considered one-sided Cp tests, so using either of those as a substitute should be acceptable if either of the spec limits are not available.
Bill Rokos Posted - 31 Jul 2014 : 12:47:45
Hello,

I will use Cpu or Cpl for Cpk.

It seems that Cp and Pp values require both LSL and USL and you do not have any special formula for single limits for this so I will just exclude them from display.

Thank you for the response.
quinncurtis Posted - 31 Jul 2014 : 10:09:23
The Cpk value is calculated as:

Cpk = min(Cpu, Cpl)

where Cpu is for the upper spec limit and Cpl is for the lower spec limit. All of the formulas we use for Cpk, Cpu, and Cpl are found in the manual.

So, if you don't have one of the spec limits, use Cpu or Cpl instead, which ever is appropriate. For example, if you don't have the upper spec limit, use Cpl because that only references the lower spec limit. Our software supports both (SPC_CPL_CALC and SPC_CPU_CALC).

this.ChartData.AddProcessCapabilityValue(SPCProcessCapabilityRecord.SPC_CPL_CALC);

This corresponds to the second reference you site. Since the answer is so simple, I don't really know why the first reference goes on about a much more complicated method, unless they simply don't have access to Cpu and Cpl.

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