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SPC advice needed

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  • #32883

    Viti
    Participant

    We have a process measure which can range from 0 (perfect) to 3 (way off). Customer’s specification is 1. Performance is at .4 mean with variation jumping around between .2 and .8 while always being better than specification of 1.0. XbarR chart looks in control but Cpk is low. Advice needed on either another metric or method of measuring this process.

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    #88354

    Gabriel
    Participant

    Why is Cpk low? If we assume that “jumping arround” variation is the process variation measured as +/-3 sigma then you have that 6 sigma = (0.8 – 0.2) = 0.6. That gives you Cp = 1.67. In the same way, 3 sigma = 6 sigma / 2 = 0.3. If the process average is 0.4 then Cpk = (0.4-0)/0.3 = 1.33. What I don’t understand is how you’ve got an average of 0.4 with individual values ranging from 0.2 (0.2 to the left of the average) to 0.8 (0.4 to the right). Is the process so skewed?

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    #88356

    Viti
    Participant

    Thanks for the analysis. Yes, the data is skewed. Heavy in the 2-4 range and light between 4 – 8.

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    #88359

    Gabriel
    Participant

    Then maybe the traditional formulas for Cp and Cpk are not the right ones. Try the following:
    Cp=(USL-LSL)/(percentile 99.865-percentile 0.135)
    Cpk=min[(USL-median)/(percentile 99.865-median);(median-LSL)/(median-percentile 0.135)], where median = percentile 50.
    If we take (just an example) LSL=0, USL=1, median=0.4, percentile 0.135=0.2, percentile 99.865=0.8, then you get:
    Cp=(1-0)/(0.8-0.2)=1.67
    Cpk=min[(1-0.4)/(0.8-0.4);(0.4-0)/(0.4-0.2)=min(1.5;2)=1.5.
    It still does not look as a bad Cpk

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