Cpk analysis for +.000/-.004 problem

[Joshua Sale]

I have an problem with a couple of people understanding if a Cpk value can be determined off of the following specifications:

Spec for hole: .165 +.000/-.004.

One person is telling me no Cpk value can be determined b/c there is no nominal spec and that this is a 1-sided specification limit.

My statistical engineer states that for Cpk analysis there is no nominal needed and the USL is .165 and the LSL is .161.

I tend to agree with the stats engineer.

Please point me in the right direction of a article or book that will state one or the other view point correctly. I need to clearly give a direction so that the arguement may end.

Thanks for your help.

[Al Rosen]

Originally Posted by Joshua Sale

I have an problem with a couple of people understanding if a Cpk value can be determined off of the following specifications:

Spec for hole: .165 +.000/-.004.

One person is telling me no Cpk value can be determined b/c there is no nominal spec and that this is a 1-sided specification limit.

My statistical engineer states that for Cpk analysis there is no nominal needed and the USL is .165 and the LSL is .161.

I tend to agree with the stats engineer.

Please point me in the right direction of a article or book that will state one or the other view point correctly. I need to clearly give a direction so that the arguement may end.

Thanks for your help.

This may help.
Calculating capability indices with one specification

[Arvind]

Unilateral tolerances are very common in engineering however these need to be converted to bilateral tolerance from process point of view.
In your case, even though design nominal is 0.165 +0/-0.04, you cannot take 0.165 as process nominal. If you do, then you run into risk bigger fraction or tail portion of population beyond specification.
For process people, the process specification needs to be 0.163+/- 0.02 which is conforming to randomly normally distributed output around the mean which coincides with target.

Arvind

[Tim Folkerts]

Joshua,

I would agree with your engineer.

Originally Posted by Joshua Sale

One person is telling me no Cpk value can be determined b/c there is no nominal spec and that this is a 1-sided specification limit.

This is not a one-side spec. A true one-sided spec would include the idea of "at least" or "at most". For example "the resistance should be at least 10,000 Ohms," or " the moisture content should be no more that 0.5%". Al Rosen gave a nice link to a webpage discussing one-sided specs where one of the limits is zero.

Originally Posted by Joshua Sale

My statistical engineer states that for Cpk analysis there is no nominal needed and the USL is .165 and the LSL is .161.

That is my interpretation, too, although I don't have a handy reference to appeal to. However, the equations themselves support this interpretation. Since the equations make no mention of a nominal or target value, all you need are the two spec limits from the customer, and the mean and st.dev. from the data.


Tim F

P.S. This points out one weakness of the whole idea of cpk. cpk measures the capability of staying within the spec limits, but in no way measures the capability of matching the desired nominal value.

Intuitively, a spec of .165 +0/-0.004 means you want the part as close to 0.165 as possible without going over, while 0.163 +0.002/-0.002 says you want the part as close to the middle as possible. If you can make parts with a tolerance of 3 sigma = 0.001, then in the first case you would want to set the nominal value somewhere near 0.164 to match the customers desire. However, making the parts closer to what the customer actually wanted would LOWER cpk from 2 to 1!

[Darius]

I am not agree with the calculation of Cpk for one sided specs

http://elsmar.com/Forums/showthread.php?t=7047

or at least the statistic can obtain confusing conclusions, for example if

Quote: (Originally Posted by Joshua Sale) My statistical engineer states that for Cpk analysis there is no nominal needed and the USL is .165 and the LSL is .161.

If you use Cpk and the process is centered on 0.163, you would obtain the best results and it's typical that nearer the target (0.165) the better.