Calculation/math to find 1.33 Cpk

D

Dave Strouse

#11
jager,

Be very cautious of calculations like this.

If customer uses this study to set specifications (and I do hope they verify against VOC), than you may be dismayed to find you cannot achieve the target in production.

Cpk is a statistic and like any statistic it has a sampling distribution.

How many points are in the study?
Is it Cpk (calculated by control chart estimate of sd) or actually Ppk(using rms sd)?

An approximate confidence interval on the Cpk is shown from this link.
http://www.qualitydigest.com/may00/html/lastword.html

More exact intervals can be calculated uding bootstrapping methods.

Note that for samples of 30 points Cpk is +/- 30%. So if you calculate a 1.33 spec limit from a sample of 30, you might be 30% off on a long term basis.
 
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D

D.Scott

#13
The easiest way to determine a reverse capability is to do a run chart and establish your standard deviation. The mean on the run is not all that important. Using the customer target mean, add/subtract 3 X std. dev. to the requirement. This will result in a 1.00 capability.

4 X Std. Dev. results in 1.33 Cpk
5 X Std. Dev. results in 1.67 Cpk
6 X Std. Dev. results in 2.00 Cpk (six sigma)

You should be able to add/subtract your process standard deviation using any customer target to determine what tolerance you need to maintain the approximate Cpk.

Dave
 
2

2nXz4u

#15
I had to do this just recently (determine what + and - tolerance we could meet based on 30 piece inspection) and found the following formula to work quite well in Excel.

For example, to meet 1.33 Cpk:
Upper tolerance = (1.33*(3*Std Dev)+Mean)-Nominal
Lower tolerance = Nominal + (1.33*(3*Std Dev)-Mean)

Where "Mean" = mean of your local inspection results, not the print (i.e. customer's) mean.

Oh, and the standard deviation needs to be calculated the old fashioned way (sum variances/n)/1.128, not using Excel's STDEV formula.

Hope this helps!
 

bobdoering

Stop X-bar/R Madness!!
Trusted Information Resource
#16
Is there a formula that will give me what tolerance I need to obtain 1.33 Cpk? For example, if my spec is .250 +/- .005 and the Cpk comes out at 1.15 and I need to be at 1.33, what tolerance do I need to obtain 1.33? Do I need +/- .006, or +.006/-.005, or +/-.007, or ???
I can go into our SPC software and put in different tolerances until the Cpk comes up 1.33, but I would like to know the math behind that. Is there a formula? Can anyone help me out? Thank you
Even though you may want to back-calculate, the assumptions are still the same: is the process normal and in control. Also, if your sample mean is not centered, is it because it can not be centered or is the sample size is too small (run too short or number of sampling points to few)?

If the sample size is too small, and the process can be centered, then you should use the target.

If the process can not be centered, then you need to take the hit and use the sample mean.

If the process is not normal - such as a properly controlled precision machining process - then the calculation exercise is fruitless, as the Cpk calculation does not apply at all.
 
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