High Capability But fails Normality

[AD44676]

Hi all,

I have been a long time reader of this forum.
I have run into a dilemma that I am hoping to get some information on how to proceed.

I have a process with extremely high process capability (cp=17.22, cpk=12.61). This is mainly due to a very forgiving customer tolerance allowance.

However, when I run a six pack CAP analysis through Minitab, my normal prob plot fails, my data is pretty close together (to the point where all the numbers are almost the same). I thought about deeper measurement resolution, however I think that would be overkill as I think anything pass 0.0000X" would be subject to too much measurement error (my resolution is 0.0000X")

I tried Individual Distribution Identification to evaluate transformations but able to get any acceptable P-Values.

Let me know thoughts. I am sure this has been discussed to death but my customer is requesting a passing result for normality.

Thank you!

 

[Mike S.]

Who cares about normality, and why?

 

[Bev D]

so you know what I’ma gonna say: your SQE is an idiot who knows nothing about math, statistics or quality for that matter. I am fully aware that TOO many people incorrectly conflate the Cpk/Ppk with a defect rate but anything beyond 95% of any distribution is unreliable (the statistical rationale is that at least 95% of the distribution is within +/- 2 sigma and the tails are “infinite” because no one knows how far the tail extends really.)

So a Cpk/Ppk of more than 2 is not producing defects (unless the process goes out of control). At your level the Customer is expecting your toothpick factory to accidentally one day make a telephone pole…

The only way to demonstrate Normailty (for some unfathomable stupid reason) is to increase your measurement resolution or lie. I would lie. A normal distribution is not going to change your Cpk/Ppk AT ALL….Your SQE is just checking a box looking for pass fail - they don’t know what any of it means…

 

[NotMe]

Firstly, it is not unusual that the Anderson Darling hypothesis test (default normal distribution test) fails. E.g. if your data is "clustered" the AD test usually fails, because the assumptions of the test are not fulfilled. There are other hypothesis test, like the Jarque Bera test, which handle such situations much better. Hence, a general advice is to ensure that you pick the correct test for your dataset. However, I reckon that this is unimportant in your case, due to the next point.
Secondly, hypothesis tests become very sensitive if the sample size is large. If our sample size is "large" it is very probable that all normal distribution tests detect a deviation from the statistical model, but that does not imply that this deviation possesses any practical relevance.
One mathematical/statistical method to argue that your system is good enough is to inflate your standard deviation by design: Suppose you have N data points in your dataset. Take the smallest and the largest value of your dataset and generate a fake dataset by using only these two values. Hence, your fake dataset contains of N data points {min, max, min, max, ..., min, max}. Now, calc the Cp/Cpk for this fake dataset. A more intuitive approach is to plot the dataset and the lower and upper specification limit. It will be "obvious" that your progress is good enough -- especially, if you state your Cp and Cpk values in the title.

One alternative is to use the Cp and Cpk formulas for non-normal distributions, see Annex E in ISO-22514-4.

Officially you don't need to check the distribution, but remember: "No free lunch in statistics!"