Specification Limits outside of Johnson Transformation

[HuefF]

Hello,

This is my first post on this forum, but I have a question that has (I hope) a quick answer. I recently did a capability analysis in Minitab, and the output is attached below. I am receiving a note that says "Specification limit or target for Centering outside of transformation function." I know what the error is telling me, but my question is how is Pp calculated if the specification limits are not able to be calculated? I would like to know an exact formula, or some reference document that explains what to do if a Johnson transformation is needed, but the specification limits cannot be transformed.

Thanks for the input.

 

[HuefF]

Forgot the output, I apologize.

 

[HuefF]

Bump please?

 

[bobdoering]

Do you have an Excel file of the raw data to look at - in time ordered sequence?

 

[Marc]

Admin note: This appears to be related to: Johnson Transformation in Minitab - How upper & lower spec limits are recalculated

 

[HuefF]

I have attached the data below. Thank you for your help.

 

[Miner]

Your process is very unstable. This may be the reason that your process appears to be nonnormal. If the process were in a state of statistical control the distribution may very well be normally distributed and your original question would be moot.

Since your process is unstable, any estimation of capability would be a snapshot only and irrelevant for predicting future performance.

 

[HuefF]

Actually, my question is more for in general and I was using this data as an example. I just wanted to know how the transformed limits are calculated if the original limits are outside of the transformation. Thank you for your post.

 

[Miner]

The simple answer is that it cannot calculate if the spec limits are out of range.

An analogy would be attempting to perform a calculation of an equation when the denominator resolves to zero. It cannot be done. Or take the Box-Cox transform. This transform does not work if the data is less than or equal to zero. What if your lower spec limit were zero? It cannot transform it.

Some transformations are open form, which like the equation of the normal distribution can handle all values. Some equations are closed, or bounded, such that they cannot handle values beyond a specific range.

 

[Barbara B]

The formulas used are explained in the help pages. Just click on the "Help" button within the process capability dialog box (bottom left) and follow the link "see also" to "methods and formulas". You'll find the attached explanation how limits for Johnson transformed data are derived there.