Implementing Cp/Cpk with only USL or LSL

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    I’m confused – if Cpk is a measure of how centered a process is, how can it be calculated with only a LSL…remembering: Cpk=min{(USL-u)/(3*sigma),(u-LSL)/(3*sigma)}; and Cp=(USL-LSL)/(6*sigma)
    What is the appropriate way to implement a valid SPC metric in this situation, and what would that metric be?



    Dear Todd,
    as you have found out, you can not use Cp with unilateral tolerances.
    You can use Cpk (selecting the one appropriate: USL or LSL). In this case Cpk is telling you whether or not you are on the right side of your specification limit. (Cpk<1, you are outside!)
    Another approach might be using Z, the distance of the process average from your specification limit in standard deviation units. That is, 3Cpk.
    Z=(USL-process average)/standard deviation, or,
    Z=(process average-LSL)/standard deviation


    Kam Gupta

    You should be as far away as economically feasible from the LSL or USL with a cpk of > 2.0. That would do it. However be careful of process variation. Higher variation and control will cause you to be farther away from the LSL or USL, which may create greater Loss, from the Quality Loss perspective (Taguchi). Hope that helps. Taguchi’s book on Offline Quality Control gives a very good perspective on this issue.
    Kam Gupta. President. Continuous Improvement Technology, Inc.. 113 McHenry Road #211, Buffalo Grove, IL 60089. [email protected]

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