Process Capability - Understanding what Process Capability Indices mean

bobdoering

Stop X-bar/R Madness!!
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#11
I know this was supposed to be a general overview of Cpk and Cp, but I wanted to point out that even when your Cpk is less than 1 (which means one or both of your upper/lower control limits are outside of the specification limit) that your data values may still be within the specification limits (i.e. - all of your parts still meet engineering conformance).
That is incorrect. Cp and Cpk are functions of the specification, not the control limits.

Cp= (USL-LSL)/6sigma; Cpk is lesser of USL-Xbar/3 sigma; Xbar-LSL/3 sigma

USL=Upper Specification Limit
LSL=Lower Specification Limit

So, a Cp of less than 1 means parts are out of specification, not out of control.
 
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D

dickgent

#12
the cpk was 26 or something!!!! what am i doing wrong -- You have done nothing wrong. A large Cpk indicates that the process is capable of holding that tolerance. The probability of producing that feature out of tolerance is VERY small. OPTION I -- You can reduce you inspection requirements for that dimension and eventually eliminate it entirely (with random checks now and then). OPTION II - Improve the part by reducing the tolerances ONLY if that will improve your product and adds value to the down line assembly or the end user.

Look for other critical to manufacture features and use your inspection resources to study (CPk) improve them.

I have said it many times Use your Cpk values as tools to identify continuous improvement opportunities.

For the previous posts
CPk = spread
CP = central tendency (centered Mean) indicates a potential nominal shift
1 standard deviation = .33333 Cpk
+-6 standard deviations = 2.0 Cpk
Hope this helps
 

bobdoering

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#13
the cpk was 26 or something!!!! what am i doing wrong -- You have done nothing wrong. A large Cpk indicates that the process is capable of holding that tolerance. The probability of producing that feature out of tolerance is VERY small.
It may also mean not all of the variation over the life of the process has been captured by the sample, or that there is sampling error. This is quite common with precision machining, die stamping, etc.
 
F

f1guru

#14
guys thank you for all the posts, its a steep learning curve we are going thru as we have never needed to look at process controls before due to what we manufacture. I think that with the tolerance we have of 0.8Ra max and all our measurements are 0.03 to 0.05 the process is well in control!!!

Thanks again it is much appreciated:bigwave:
 
D

dickgent

#15
OK .... now you changed things... :rolleyes: If you are studying Ra then it is a unilateral tolerance (cannot be less than zero). Therefore only 1/2 of the normal curve applies. You can use the Cp and CPk calculations for unilateral tolerances as described elsewhere on this site. Good Luck to you.

http://elsmar.com/Forums/showthread.php?t=6552
 

bobdoering

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#16
OK .... now you changed things... :rolleyes: If you are studying Ra then it is a unilateral tolerance (cannot be less than zero). Therefore only 1/2 of the normal curve applies. You can use the Cp and CPk calculations for unilateral tolerances as described elsewhere on this site.
"Half of a normal curve" does not apply.

First, it is an inadequate model - as it does not fit the data adequately at all. Weibull or beta generally are a much better model of unilateral tolerance behavior.

Secondly, calculating Cpk based on only one of either Cpu or Cpl is generally meaningless. Cpk is specifically designed to tell if the distribution is centered. So, first, it needs to make sense that it is centered, which it does not make sense with a unilateral tolerance with the target at zero. What it actually describes is the distance the mean is from the tolerance. That is a totally different question than if the mean is centered. So, just because you can calculate it, does not make it meaningful.

I used to use half normal, until I learned more about the applicable statistics. It is a common approach for people trying to meet a customer's rubber stamp request for Cpk on any and every kind of characteristic. Unfortunately, it is incorrect.
 
B

bearfan454

#17
You could tighten the spec limits. It would lower the cpk value but it would also show continuous improvement.
 

bobdoering

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#18
You could tighten the spec limits. It would lower the cpk value but it would also show continuous improvement.
Not always. For precision machining, that reduces stability by requiring more operator intervention and more adjusting - so the idea of reducing the control limits is not always "continuous improvement". Continuous improvement for precision machining is decreasing the tool wear slope - either with better tooling or improved process parameters.

And you should never tighten the product spec limits. They are design limits - and their meaning should represent the area under the the Taguchi loss function curve (calculated for that specific characteristic) where the dimension actually works - by design. You can tighten process specification, but never print specs. You will lose extremely valuable data that has a specific meaning.
 
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