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Topic Capability Calculation After a Johnson Transformation of Non-normal Data

Capability Calculation After a Johnson Transformation of Non-normal Data

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This topic contains 4 replies, has 4 voices, and was last updated by  Chris Seider 11 months, 1 week ago.

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  • #698987 Reply

    Reputation - 22
    Rank - Aluminum

    Hello everyone,
    I am a quality engineer with almost no statistics background.
    For process evaluation, I use Minitab in my job.
    I’m stuck with the current problem. As illustrated in attachement, some of my tests failed the normality test. So the capability can be affected.
    As I would like to assume that my process produces normal data (90% of the tests produced normal data), I did a Johnson transformation.
    On the left column, the Johnson transformation defined a “transformed” LSL (low specification) and gave a recalculated Cpk (which is lower than the “raw” Cpk).

    On the right column, the Johnson transformation couldn’t define a “transformed” LSL (probably because the formula is about y=Ln(x-A) with a A>LSL). Then Cpk is given and is higher than the “raw” Cpk.

    What is the solution to have a easy/quick ppk estimate?
    -try other non-normal distribution ? (but the histogram shows that my process is almost normal). Additionnally, some of my other samples couldn’t fit any proposed distribution.
    -perform a manual Johnson transformation y=Ln(x-A) with a A just above LSL? p will be affected but is it a problem is p=0.06 instead of 0.1?
    -my sample size is 50

    Thanks in advance.
    Kind regards,

    Note :
    -only some of my results are not normal. Other a perfectly normal.
    -I assume that non normality of the attached example come for an undetermined external effect which can’t be back traced (I tried to investigate the non-normality cause but all tests were performed in a limited time space, with the same equipments, with the same raw materials, with the same manufacturing parameters….). I don’t have the time to further investigate and would like to give a status on the process

    #698993 Reply

    You’ll get similar thoughts from others but I’d NEVER advocate Johnson transformation for real world situations. I find the “formula” to be confusing and specs don’t mean anything anymore. If possible, find a better fitting natural distribution and do the capability analysis assuming that one.

    Worst case, if you have lots of different peaks of data, then just use the manual method of calculating ppm defective and convert that to a sigma level if the organization knows about sigma levels or you can do the quickie calculation from Z overall to Ppk or Cpk.

    Two cents to have over a coffee. :)

    #698996 Reply

    Just looking at your normal probability plots the one on the left look bi-modal and the one on the right looks tri-modal. You might want to look at the data associated with the straight line portions of both of those plots to see if there are any obvious differences between the groups.

    #699103 Reply

    Paul Keller
    Reputation - 35
    Rank - Aluminum

    Hopefully you’re aware that capability analysis is meaningless without first verifying the process is in control. If the process is out of control, then there is not a single estimate of the process mean and/or the process standard deviation that provides a meaningful estimate for that process. An out of control process has a shifting mean and/or standard deviation. Likewise, there is no single distribution for the out of control process.
    Minitab’s Johnson transformation is useful, but a little complicated. If you could provide your raw data in a Minitab file I could walk you through the analysis.

    #699268 Reply

    Great reminder to the original poster…

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