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Acceptable P/T

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  • #48377

    Emily
    Participant

    I know that acceptable P/T ratios are less than 30%.  what if a P/T ratio is higher than 30%, is there a way to estimate alpha or beta errors.  ie, accepting bad parts or rejecting good parts. Can you explain?

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    #162840

    Mikel
    Member

    Something to think about – You really want to make decisions about P/T ratios in conjunction with what you know about your capability and control.
    For example, if you had a process where all of the variation came from the measurement system (think more in terms of the variation due to the process is small compared to the variation due to the measurement system); it would be possible to have a P/T of 50% and still have a Cp of 2. The point there is if you have great capability and the process stays to the center, you may not need to worry about the measurement system the risk of accepting bad or rejecting good are very, very small.
    You can find the probability of rejecting good or accepting bad by figuring out how much of your distribution overlaps the spec limits and look at the variation of the measurement at those limits.
    The safe thing to do is to guardband if you cannot get an acceptable P/T if you capability is not good. If you are the supplier, bring in your spec limits by 3*std dev of the measurement system.
    If you want to give an example of actual capabililty (Cp and Ppk) and actual P/T, I’ll walk you through how to quantify the risk.

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    #162841

    Emily
    Participant

    thank you for your reply.
    Let’s assume the calculated P/T is 50% and process capability is Cpk of 1.92.  How do I calculate the two rates.

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    #162842

    Mikel
    Member

    I’d need to know Cp as well. Cpk doesn’t inform you about the width of the distribution.

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    #162844

    Mikel
    Member

    Let’s assume Cp = Cpk since the Cp cannot be worse than 2 if P/T
    = 50%.Set up a spreadsheet that shows the probability of any given
    reading. To make things easy I assume a spec with of 1 which
    would make my Std Dev = .087. I set up a table going from 0 to 2
    (I am assuming my spec is 0 -1 and I am going to 0 -2 figuring the
    probability of anything in increments of .01). Figure the probability
    of all the increments of .01 – this can be done in Excel. then figure
    the same thing if it were caused by the measurement system – for
    example, I got a reading of .5 but it was really > 1. Multiply the
    probabilities and add. 1. Multiply the
    probabilities and add. 1. Multiply the
    probabilities and add.This could also be done as integrals, but I haven’t got the time to
    figure that out. This is a reasonable approximation.I get that the probability of saying it’s good (reading between 0 and
    1) when it’s not is about 12 in a million. Saying its bad when it’s
    not is about 4 in 10 billion.

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    #162852

    Mikel
    Member

    This can also be done as a Monte Carlo simulation. 5 – 10 million
    passes where you have the two distributions and the resulting
    measured value should show values in the same neightborhood.

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