How to Do Ppk on Non-Normal Data

M

mechhari22

#1
In one of the gears we manufacture PCD Runout w.r.t inner diameter is a KPC parameter. I did Pp & Ppk calculation in the regular way, plotted a histogram and I sent the same to my customer. But he said I need to follow “NON NORMAL DISTRIBUTION”. Can any one tell me what it is, and how to do it
 
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bobdoering

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#2
Re: How to Do non normal distribution

Can you supply us with an Excel spreadsheet of your data for us to look at and analyze?
 
M

mechhari22

#4
Re: How to Do non normal distribution

Hi BOB,

Thanks for your reply, attached data sheet for your reference. The parameter is run-our, were the spec: is 0.075mm Max ie, 0 -0.075mm. Now in this case I have calculated Pp PPK assuming 0 as LSL & 0.075 as USL. Pls tell me if my assumption is ok.


0.031
0.032
0.04
0.032
0.028
0.023
0.03
0.037
0.04
0.012
0.031

0.03
0.031
0.03
0.034
0.026
0.017
0.036
0.027
0.017
0.03
0.036
0.032
0.042
0.034
0.03
0.034
0.029
0.026
0.04
0.026
0.035


Sorry i am unable to attach the ecell sheet, could not find the provision for it
Regards,
Hari
 
M

mechhari22

#5
Hi Marc,

Thanks for the links, so much of useful information, but could not find any discussion about run-out. My specification for run-out is 0 – 0.075 mm max. In this case I understand the LSL is 0 & USL is 0.075mm, the mean value is 0.0375. But the problem is in regular data, closer to the mean is better process, but for run-out LSL (ie 0 run-out) is the best process. Pls tell me how to go about this.

Regards,
Hari
 

bobdoering

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#6
OK, I did the distribution analysis on the data, and attached it. I also attached the excel file for anyone else that cares to have fun with the data.

The data shows that there are better distributions to model your data than the normal distribution (Johnson Family p-value 0.85, normal p-value - 0.06) Either of the analysis shows the process capable - more so when using the model that more closely represents your data.

There is some interesting points near zero - and I wonder if there is some measurement error of some sort. Even so - so far, so good.

By the way, it is not "closer to the mean" that is a better process, it is closer to target. Your target is 0 - the closer the better. The closer, the less normal, too. Your data is non-normal, but not because it is close to zero - the skew is in the wrong direction for that. Something else is going on.
 

Attachments

Last edited:

bobdoering

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#7
You might want to look at what happens of you make 0 a lower specification (see attached). The calculations will assume your target is half way between the specifications, thus making your Ppk calculations look worse. But, your target is not between, it is 0. That is why the previous approach - distance from UCL - is more appropriate of an estimate of capability.
 

Attachments

M

mechhari22

#8
Hi Bob,

I am not a statistician I am a technical person, so I am finding it difficult to understand your reply. I normally go for Anderson darling Method to test normality, in this subject set of data for run-out I got P value = 0.074 which is greater than 0.05 so I concluded the process is normal.

But you have done some high-tech analysis which I am un able to understand, could you Pls help me out in understanding the method you have used.

Thanks &Regards,
Hari
 

bobdoering

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#9
I normally go for Anderson darling Method to test normality, in this subject set of data for run-out I got P value = 0.074 which is greater than 0.05 so I concluded the process is normal.
When looking at goodness of fit statistics, what you are determining is the probability of whether the data does not fit the specific distribution. In Charles Annis page on Anderson-Darling, his Note 1 does a good job of explaining what you are really looking at. You really are not supporting that you have a normal distribution, you are supporting the probability that you do not, and for your data using that one calculation you are not rejecting that you do not have a normal distribution - a much different term than concluding you do.

The process I use is the "Distribution Analyzer" , which calculates the goodness of fit for a series of common distributions, and gives you the result of the distribution with the highest p-value. (I believe this is similar to the Pearson analysis.) The logic then behind that is the highest p-value curve has a lower probability of being rejected as the specific curve. So, it looks at several distributions, rather than making a judgment towards just one.

That is why I prefer it. As you can see, the tool also permits me to show the data and curves for any of the distributions - which is handy. If the best curve p value is very close to the normal curve's p-values, I may assume that it is "normal enough' to suit my statistical intentions.
 
M

mechhari22

#10

Hi Bob,

Good explanation, now I understand why is should not have used Anderson darling method. I just got the distribution analyzer software pretty good one.

The software says the best distribution to analyze my set of data is Johnson family distribution.

One thing I found in both Johnson family analysis (one with no LSL & the other with zero as LSL) is the P value remains same. Assuming the limiting factor for P value is 0.05 my process is well with in normal distribution in both the cases. So can I say my process is normal?

Also I see there is no Pp value indicated if we do not specify LSL (in this casse the Ppk is good), can you explain me why it happens? I understand if we do not give LSL then the Ppk value should not be shown since it the capability index (shows the centering of the data closer to the mean/target). Were as the Pp is the capability value which needs to be indicated for any set of data, Pls correct me if I am wrong.

The Ppk value becomes worse if we specify zero as LSL, so you have suggested not to go by this method, Pls explain me how you arrived at this conclusion.

Bob thanks a lot… Expecting your continuous supper

Thanks & Regards,
Hari
 
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