Is a Target Outside Range of Xform Function Bad?

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This topic contains 3 replies, has 4 voices, and was last updated by  Robert Butler 6 months, 2 weeks ago.

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    Hello, all. First time poster with a question about a message that came up in Minitab when doing a Johnson transformation on some supplier data. My supplier’s data in non-normal and, without getting into all the details, this isn’t surprising to me given the process and allowed range. So in order to calculate a cpk/ppk, I used a Johnson transformation. The transform worked (at least it didn’t fail to transform, and gave me revised values for pp/ppk); but it didn’t recalculate the spec limits, and I got this warning message: ” Specification limit or target outside of range of transformation function.”

    My question, does this mean the transformation is no good even though I got new pp/ppk numbers? I would think if there were an error of significant magnitude, it wouldn’t attempt to re-calculate pp/ppk. Should I rather go with a non-normal analysis and cpk/ppk numbers (Weibull, SEV, etc.) since they also give acceptable, although much lower pp/ppk numbers?




    Chuck White

    I would definitely take that warning as a red flag. It basically means that if your data had included any measurements at the spec limits, the current transformation function could not have been used. Since I would expect measurements at spec limits to be possible, I wouldn’t put any trust in this transformation.

    One possible cause for the error is that you put a boundary in as a spec limit. For example, GD&T dimensions like roundness or flatness can never go below zero, so zero is a boundary, not a spec limit. If that is the case, in Minitab you can either check the Boundary box for that limit, or you can leave the limit empty (both options will give you the same result).

    Also, the Johnson transformation is complex compared to other normalizing methods, so it should only be used as a last resort. The keep it simple principle applies. Did you try a Box-Cox transformation, or fitting the data to another distribution first?


    Chris Seider

    I’d not bother doing Johnson transformations to get a Cpk….you can always look at ppm defective or IF required convert the ppm defective to a Ppk or Cpk depending on the source of the data.


    Robert Butler

    The other option is to not bother with any kind of transformation. Since you know the distribution is non-normal for data when the process is in control just use the usual methods for calculating Cpk for non-normal data. It is my understanding that Minitab has this method as part of the program. The method is described in detail in Chapter 8 of Bothe’s book Measuring Process Capability. The chapter title is “Measuring Capability for Non-Normal Variable Data.” Personally, when having to generate a Cpk for non-normal data, it is my method of choice.

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