Plotting Cpk as Function of Measurement Event

W

wilburgizmo

#1
I have been thinking of ...

Calculate Cpk based on the most recent 25 data / measurements and then record that Cpk value. Then re-calculate Cpk every time another measurement happens.

Then plot those Cpk's (Y-axis) as a function of the measurement event (increment the X-axis by 1 unit).

Has anyone found this to be a useful or insightful technique or graph?
Or possibly, is this technique a statistical confusion without merit?

Thank you for your time and thoughts.
 
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bobdoering

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#2
I vote for this technique as statistical confusion without merit. The Cpk is a crappy number to begin with - one number attempting to describe all of the historical variation of a process. You are better off focusing directly on the measurement that needs controlled to be capable. Make sure your measurement system is effective - the gage and the technique - or any data you get is not worth evaluating.

It is good that you are pondering these things, though.
 

Miner

Forum Moderator
Staff member
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#3
I agree with bobdoering that plotting Cpk has little value to add in the short term. I do think that establishing and understanding the confidence interval for Cpk is worthwhile.

Given that Cpk is comprised of a mean which has uncertainty and a standard deviation which has uncertainty, it is important to understand that the Cpk also has significant uncertainty. Your calculated Cpk of 1.34 may have a 95% confidence interval of 0.98 to 1.70. See Size Matters: How good is your Cpk, really? for an article on calculating confidence intervals for Cpk.

Beyond that your control chart will ensure that any process changes that will impact the Cpk are detected. If your process is in a state of control, your Cpk will also be in control.
 
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Bev D

Heretical Statistician
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Super Moderator
#4
it's also kind of like transforming your data. Cpk is a (very poor, littel statistical merit) measure fo capability. Why not just plot your individual data poitns against the spec limits? that will very clearly and directly show yoru capability. no need for translation, explanation or statistical voodoo.
 
D

Dave Dunn

#5
it's also kind of like transforming your data. Cpk is a (very poor, littel statistical merit) measure fo capability. Why not just plot your individual data poitns against the spec limits? that will very clearly and directly show yoru capability. no need for translation, explanation or statistical voodoo.
I would have to disagree. Plotting points against the spec limits is not an indication of capability unless you are planning to measure and plot each and every part, and even that isn't a measurement of capability - that's just go/no-go gaging. You could have several parts of a sample very close to the spec limit and others near the centerline, and though all your points would be in spec, you would not be in control, much less capable. I think the best you could get with an individuals plot against the specs is some idea of process spread and trends, but that's about it.
 

bobdoering

Stop X-bar/R Madness!!
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#6
Look on the bright side, you have figured out a clever practical joke to the SPC practitioners that swear there is no relation between capability, specifications and SPC! :lol: Of course, that notion is not always true anyway...but this really nails it!
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#7
I would have to disagree. Plotting points against the spec limits is not an indication of capability unless you are planning to measure and plot each and every part, and even that isn't a measurement of capability - that's just go/no-go gaging. You could have several parts of a sample very close to the spec limit and others near the centerline, and though all your points would be in spec, you would not be in control, much less capable. I think the best you could get with an individuals plot against the specs is some idea of process spread and trends, but that's about it.
I guess we will have to disagree then. I think that understanding my process spread and trends (or components of variation) are not trivial. plotting your actual results tells you what your actual performance is. if you are plotting only sample data you would have to have more than one sample set, and that would tell you the relative spread of your process rather than relying on some arbitrary selection of a distribution...I think too often we think (wish?) that statistics had some magical power to be omnicient and all predictive. several very influential statisticians have said: plot your data, look at your data and think about your data. I have found this to be the most powerful statistical analysis for most industrial manufacturing applications. that's *my* experience.

and I made no statement concerning control but then again neither did the OP.
 
W

wilburgizmo

#8
Maybe I could plot these Cpk's on on a trend chart, evaluate for process cabability, apply SPC control limits for the cpk's, and then calculate new running Cpk's on the original Cpk's - etc etc - would this be more beneficial?
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#9
Maybe I could plot these Cpk's on on a trend chart, evaluate for process cabability, apply SPC control limits for the cpk's, and then calculate new running Cpk's on the original Cpk's - etc etc - would this be more beneficial?
no....
what are you trying to learn or accomplish or demosntrate?

*my* suggestion would be for you to go to 'first principles' and understand what process control and process capability are all about. understand the limitations of the 'Cpk' calculation. (Such as the requirement that the process be in statistical control AND have a Normal distribution. most processes do not have Normal distributions (read Bert Gunter's series in ASQ Quality Progress: Gunter, Bert, “The Use and Abuse of Cpk, Parts 1, 2,3 and 4”, Quality Progress, January 1989, March, 1989, May 1989, July 1989)

then simply plot your data: read about multi-vari to helpng determining appropriate sample sizes and sampling frequencies. learn about your process variation without the confusing and obsfucating effects of summarized, manipulated and spindled data....
 
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