Software Calculation Errors for Cp and Cpk With Unilateral Tolerances

[Caster]

I have looked back through the archives for Cp and Cpk on unilateral tolerances, and I still need some help.

We now have a situation with our SPC software when it determines capability for unilateral tolerances. The software supplier has offered to fix this if they can get a definitive ruling on what is correct. So here’s your chance.

Here is an example.

Iron content in Aluminum is 0.25% MAX (upper spec limit). Our data averages 0.10%.

Here is my understanding (please correct me)

This software seems to assign 0 as the lower spec limit. This is hard coded, no option to change it.

Process capability (Cp) should not be determined since there is no tolerance as such.

However, the software can mathematically determine Cp by using 0 to 0.25% as the Tolerance.

I believe Cp has little meaning in the case of unilateral tolerances – am I right?

A better measure would be the Taguchi loss function, since it equates loss(cost) to how far from (close to) ideal you are.

Process Capability Centered (Cpk) is even worse.

The software will take the lesser of AVG- LSL or USL-AVG and produce a “mathematically correct” Cpk value.

I believe this is wrong since it results in a poor Cpk, since our process averages much closer to 0 than to the USL.

I believe the Cpk calculation should only be determined for USL in the case of a unilateral tolerance – am I correct?

Interestingly we also have MiniTab, and it seems to do things correctly (if you set it up right).

Minitab will calculate a Cp if you enter 0 as the lower spec limit. However, if you leave the LSL blank, Minitab will not report a Cp value. This makes sense to me.

Also Minitab will calculate Cpk from the USL if you leave the LSL blank. However, if you enter 0 it will report the lower value.


Looking forward to an intense learning experience


Caster

[Paul F. Jackson]

Check the distribution for normality, use Minitab, and leave the LSL blank like you said or get the fix for the other software. I think that you have already found your own solutions to the problem.

[Darius]

Caster

If your software takes 0 as the other specification buy another one. It's like sometime ago I told someone, it's like using a table without all the background or objective of it. If Cpk is calculaded by the software the way you said it's even worse.

I like to see someone that likes Taguchi Index as an indicator, the Cpmk could help more than the cpk for one spec conditions. Why, because Cpk is as you said CENTERED.

You said

I believe the Cpk calculation should only be determined for USL in the case of a unilateral tolerance – am I correct?

if you only have one spec you at least do it with the only one that you have, but IMO it's as you said better to use Cpmk. Or nonparametrical if your data behaves non gausian ("normal").

[Arvind]

Please take a look at this 10 page document from Minitab which clarifies many queries and gives formulae for questions you raised.
http://www.minitab.com/support/docs/...alFormulas.pdf

Hope this helps.
Arvind

[Arvind]

Many types of data, for example- flatness, runout, impurities or material composition which has one sided limits is observed to be non normal. The reason for non normality in most cases is likely to be
a) Outliers
b) bimodal or multimodal data
In such cases, normality assumption and calculation of capability can give errors which may not be desirable.

It may be desirable to fit Weibull distribution and find shape and scale factors (which define Weibull) from the data and find how much of tail portion of distribution exceeds the threshold limit.
Many times fraction of population exceeding specification is of importance than capability by itself.

Arvind