Cpk after Data Transformation - How to Transform LCL /UCL to get Capability Report

L

lacarrye

#1
Hi!,
I will appreciate any help on this. I have 120 values (Injection Time), which has as UCL < 5 secs. LCL<0, I ran a normality test on Minitab and the best p value is shown after Johnson Transformation. So far so good! Then I'm wondering how to Transform my LCL /UCL to get my capability report. Im wondering if I'm forcing the statistics to get what I think I need and not what I should to do.

Thank you!
Javier
 
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Miner

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#2
Re: Cpk after Data Transformation

Analyze your "untransformed" data using Capability Analysis (Normal Distribution) then select the Transform button and select Johnson transformation. This will transform both the data and the spec limits.

Another option is to download Minitab's macro for nonparametric capability analysis. It requires a minimum of 100 measurements, which you exceed.

I am always concerned when the Johnson transformation is the only one that works. Many processes do have non-Normal distributions, but should match the more common distributions such as Lognormal or Weibull. When they do not, it makes the probability of mixed process streams or out of control processes more likely.
 

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L

lacarrye

#3
Re: Cpk after Data Transformation

Thank you! Miner,
I followed your recommendations. This is interesting, cP/cpK are higher with NO Transformation. No clue.

I appreciated your help. Javier
 

Miner

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#4
Re: Cpk after Data Transformation

Can you attach you data? It's always easier to give good advice with some data to analyze.
 
L

lacarrye

#5
Re: Cpk after Data Transformation

Hi! Miner,
Thank you! Again. Please, see attached xls.
regards, Javier
 

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Miner

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#6
Re: Cpk after Data Transformation - How to Transform LCL /UCL to get Capability Repor

Judging from the Histogram and control chart, the lack of Normality may be caused by lack of process control. In the second histogram, I added a normal fit centered on the median value and estimated a standard deviation. Notice how well the distribution fits with the exception of the right tail, which would be out of control points.

The last is a Normal probability plot with values > 2.6 removed.
 

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Steve Prevette

Deming Disciple
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#7
Re: Cpk after Data Transformation - How to Transform LCL /UCL to get Capability Repor

Keep in mind, with the process being "not in control", and Cpk values are meaningless as you are unable to predict future results.
 

bobdoering

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#8
Re: Cpk after Data Transformation - How to Transform LCL /UCL to get Capability Repor

Also remember cramming data into a statistical model is not the first approach to understanding capability. The first step is to establish the "total variance equation", developing a CNX analysis, then attempt to control the controllable variables. Then perform your capability analysis run. If you don't do that, your data is just stew. Most processes are multimodal (the total variance equation supports that). Being "in control" means lack of special causes - not normal, not unimodal- unless that is the expected distribution for that process.
 

Bev D

Heretical Statistician
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#9
Re: Cpk after Data Transformation - How to Transform LCL /UCL to get Capability Repor

Let's think about this differently: why do you want to calculate Cpk? what value will this index give you? What are you trying to accomplish by studying this process?


many processes are simply Not Normal (time is often not Normally distributed but can be quite stable) even unstable processes can be improved before 'removing the causes of instability'...

you state that the data is 'injection time', can you elaborate?
 
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