Capability - How to calculate Capability Indices for Non-normal Distributions



:bigwave: Thanks god i found this site
Here are my questions: are there any stats genius out there tell me how to calculate capability indices for non-normal distribution? such as best fit Jonhson for for Pp and Ppk . what is a ordinate .99865 and ordinater .00135 ( where do i find this value what book etc..) can it be manual calculated?
it would be more helpful beside johnson dist. what are the other method to calculate process capabily for non-normal (manually)
One more thing if the process is not follow the normal distribution Cp and Cpk can't be use right? is it the same with if the control chart is running like a yo-yo Cp and Cpk indices can't be use right?
thank you for your help
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Rick Goodson

Welcome to the Cove.

First, I am not sure there are any statistical geniuses here, but I think we can help nevertheless. Unfortunately your questions tend to run on a bit. Could you give us some additional background. What type of process are you running and how have you determined it is non-normal? You also mention a control chart that is running like a "yo-yo". What type of chart is it; X-bar, R, s, Individual X? Charts can look like a "yo-yo" for many reasons; wrong scale, bimodel process, mixed samples from two universes, etc. Describe the process for us and we will try to help.


we are in a automotive industry for GM
The chart that we are using is Xbar and R chart. The reason I said it's not-normal is that it's bimodal on the histogram, and the ±3 Standard deviation is greater than the specification limits and the we still have the Cpk of 2.156 If we assume the data is a normal distribution. By the look of that I don't think the data is normal so assume it normal may mislead the true capability. our SPC software give us the option to choose normal or Johnson curve if the data is not normal. I really don't know much about the Johnson curve, I have the formula but i don't know how to apply it to the data
Thanks for your help

Atul Khandekar


One more question. Have you tried to investigate why the data is bimodal?



lisaptran, you said

"The reason I said it's not-normal is that it's bimodal on the histogram"

BiModality in histogram charts could be because of wrong number of frequency bars, it's not a test for normality.

and also

" the ±3 Standard deviation is greater than the specification limits and the we still have the Cpk of 2.156"

Strange, I am curious about it, I tink, it's not posible for Cpk to be greater than 1 with the 3 Standard deviation greater than the spec limits.

There are still, non parametric Cp and Cpk using the percentile of your data and transformation methods for data (like box-cox, my favorite), but I tink your explanation looks a bit strange.

The yoyo behabiur on a SPC chart is mostly because of different process conditions/specs or raw material.

Could you supply us a set of your data?



There was a big different per operator when shift change. However if i know that was the cause what should I do with the data for the mean time? i know operator need to re-train or something like that but what can we do with the data?
thanks for your response

Atul Khandekar

This seems to be an MSA problem. As you said, operator training would help reduce the problem in future. Also, you could investigate what happens at 'shift change' .

As for the past data, I am not sure what you can do with the data that is obviously erroneous. Can you classify the data operatorwise?


oh so Non-normal analysis is only apply for unilateral spec. i thought it also work for bilateral if the data on histogram look crazy. in my case i believe we can segregate per operator but the problem was not enough data for analysis if segregate per shift. That was why I combine all shifts. By the way what is Johnson curve and when do we use it?
thank you

Dave Strouse

Get a grip on the process first!

For Johnson curve info try this link -


Your data are not under control. You have a mixture distriibution.
Fix it before you proceed. :bonk:

One of my heroes Dr. Don Wheeler asks in one of his books Understanding Statistical Process Control.

"What can be said about Unstable Processes?"
Answer - Not much!

Get that book and read it, please. Especially the part on capability confusion.

In one post you said that your three sigma spread exceeded the specs, but you had a Cpk of over 2!

Either you arer not calculating correctly or you are "hosing" us as the immortal McKenzie brothers say up there.

Are you hosing us, EH!:vfunny:

(close enough to the Great Northern Country to love it!)
and it's sunny today :cool:


Dave Str..
Don't vfunny: :vfunny:
I guess you are confusing about Cpk and Ppk... Cpk calculate base on the Rbar/d2 ( this is sigma hat and Ppk is calculate base on the standard deviation (S) in manufacturing process we only use Cpk... why? i dont' have to tell you that...
The reason why Cpk is good and standard deviation is still exceed the Spec is the mean±3S has nothing to do with the Cpk calculation.
bonk: :bonk: :bonk:
Here is something for you to do
Spec limt is 22.04/22.00 mm
Standard deviation is .009 mm ( this is on the histogram) but has nothing to do with the Cpk calculation
sigma hat .003 for Cpk calculation
Mean 22.018

are you :confused: now?
I guess you are not in a real manufacturing world of SPC here is the source AIAG SPC manual :biglaugh:
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