Non Normal Data Transformation(Capability Analysis)

[#1]

Hello All,

I have a lot of Non-normal Data so i read how to use Continuous fit and Fit All,please see below Eg. Figure 1.

Now I have to enforce our Specs of 8.4-9.2 , so first i transformed the data by picking Log Normal (Using"Save Fitted Quantile") Figure-2 because Johnson-Si & Johnson Su showed a very weird peak.

Now i am wondering :

1) Did i pick the correct transformation

2) If yes, do i need to transform the Spec values of 8.4 & 9.2

3) Is it correct to use the capability analysis on transformed data as the data is still not normal (shown by Goodness of Fit)

Please advise 

Thanks in advance  

[#2]

@RBAero,

You did not mention which version of JMP  or JMPPro you are using. The link below provides a step by step example if you have the Process Capability platform on your PC. You have the option to Set Distribution or use Best Fit.  PPK, using maximum likelihood estimates of percentiles is an often used choice.

Note, PPK as well as Cpk calculations, assume identically and independently distributed data ( IID ), meaning no systematic variations. 

Hope this helps.

JMP Documentation for Nonnormal-capability-analysis 

[#3]

Thanks for the reply,
I am using JMP 14.
I did use the above method its very helpful and intuitive

[#4]

I think a 'best practice' is to select a distribution model based on knowledge about the process that generates the data, rather than 'best fit' criteria. The criteria are based on a single sample. The knowledge is based on the population.

Note that if you fit the distribution in the Distribution platform, the red triangle menu for the fitted model contains a command to initiate a process capability analysis for the non-normal distribution. You do not need to transform your specification limits in this case.

[#5]

I guess I wouldn't get too hung up on worrying about which transform, any process capability index, or any other statistic associated with the practical problem at hand. The process is woefully incapable...a conclusion that isn't 'statistical' in nature...but a cursory inspection of the data untransformed with spec limits overlaid shows that the preponderance of data is outside the spec limits. I'm presuming your process is steady and stable, devoid of assignable cause variation. If that's the case, now on to the hard part...either reducing variation. Or maybe a first step is questioning the validity and applicability of the specification limits. Do they reflect some real life criteria? Regulatory, supplier driven, customer driven, industry standards/specs driven? Or were they determined by the 'we really have no idea what appropriate tolerance values should be...so in an effort to force manufacturing to 'aim', we'll just use aim as the center of the spec range...and go plus or minus 10% from there.'

Don't laugh...I saw this thinking applied often in industry.

[#6]

Thanks
I did make me Laugh, as the Spec limits have been in fact designed the way you said for above process,
So our challenge at hand is to challenge the limits and rethink whether these are applicable or not in real world.
We tested for Normality which it doesn't passes.
I read a lot on using Control Charts with Non-Normal Data and i know that we can use Control chart irrespective of the nature of the data.
So, now i have Control Limits based on the data in hand.
I wish to use those limits and compute the Capability Indices and make a comparison between the Spec Limits and Control Limits.

[#7 · Accepted solution]

OK...here's a thought for you. Have you considered running a designed experiment where the levels of the characteristic in question at the  1 and 99% quantiles of your data range are starting values for high and low for that factor? And maybe add some other factors that are relevant for the key output characteristics? Of course you'd have to use the variable you've plotted here as a factor and not a response within the context of the experiment. And find some meaningful fitness for use characteristics driven by perhaps customer end use needs. You don't even have to run a multi factor experiment...although it could yield enormously valuable information...especially if this single factor interacts with others that are influential in the process overall. I'll also send you a private message.