Estimating Sigma for Capability Metrics: Industry Standards?

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    I am back after a year, with another question regarding SPC.

    I was recently surprised to learn that my traditional CPK formula was improper. I had simply thought the formulae for the metrics used the sample standard deviation. Oh how terribly misinformed I was….. Misinformed. That seems to be a common theme here in the world of SPC. I’ve never seen a topic so misconstrued and incorrectly taught in my life. Someday the world will realize you can’t try to use statistics if you don’t know anything about them… I digress.

    My question…

    I was rudely awaken with the 6 different estimators for the POPULATION SIGMA, which is utilized in the CP/CPK formulae depending on whether we subgroup or not.

    Thus, when subgroup size = 1, sigma is estimated with either:

    When subgroup >1, then estimators are based on either…

    Some of these, of course, are divided by hartley’s constants…

    My question is…
    Which is correct? I work in Automotive, so AIAG is preferred. However, i don’t care to open up the AIAG manual at the time, and i’m also curious to hear professional’s opinions on what industries require what. I also understand, the customer may have a unique preference. Whats your experience and which are less common estimators?

    Thank you


    Iain Hastings

    The AIAG calculations are based on a “Significant production run” as detailed in the PPAP manual. A significant production run is 300 parts manufactured under production conditions.
    The required calculation is for Cpk using the standard deviation estimated using Rbar – this assumes a stable process. The PPAP manual does allow an alternative for an unstable process (with identifiable trends or patterns!) in which case Ppk should be used – ie using the sample standard deviation.
    The idea of calculating indices on an unstable process is somewhat contentious – Douglas Montgomery would liken it to “statistical terrorism”. The key point in the AIAG manual is the predictab;e trend or pattern.
    Note that although this is what is contained in the AIAG PPAP manual, Customer-Specific Requirements may differ. For example, I believe that Ford requires using the sample standard deviation for calculation.

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