process capability on one sided specification

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    Good day. im just confusing of what process capabiltiy index to use when their is one sided specification only. Please help me.
    Email me at [email protected] for some suggestions and comments . I’ll appreciate all concern. Thank you very much



    Hi George,
    For a feature with only an upper spec limit (USL), use the following, where mu-hat is an estimate of the process average and sigmaST-hat is an estimate of the short-term process standard deviation (usually estimated by R-bar / d2):
    Cpk-hat = (USL – mu-hat) / (3 sigmaST-hat)
    If the feature has only a lower spec limit (LSL), use the following:
    Cpk-hat = (mu-hat – LSL) / (3 sigmaST-hat)
    If you prefer to estimate long-term capability, estimate sigmaLT with S-total / c4 and use the following:
    Ppk-hat = (USL – mu-hat) / (3 sigmaLT-hat)
    Ppk-hat = (mu-hat – LSL) / (3 sigmaLT-hat)
    Of course, before estimating process capability, the process should be stable, as demonstrated by an appropriate control chart.  In addition, the above formulas assume the process output is close to a normal distribution.
    Hope this helps.


    Robert Butler

      If you are dealing with a unilateral tolerance and your measure is non-normal (e.g. taper, flatness, surface finish, concentricity, eccentricity, perpendicularity, roundness, straightness,squareness, weld bond strength, casting hardness, shrinkage, hole location, parallelism, etc) then you will need to use the following:
    Equivalent P’pu = maximum{ (USL-T)/(x99.865-x50), (USL-x50)/(x99.865-x50)}
    x99.865=the value at the 99.865% point of the data when plotted on normal probability paper
    x50 = value at the 50% point of the data when plotted on normal probability paper.
    T = target of the process average
    For further reading you should check Bothe – Measuring Process Capability pp.445-447



    I do not agree that all of those measurements are non-normal. Why would you suppose that they are ?


    Robert Butler

    The list of measurements  is a direct quote from pp. 431 of the Bothe text. 
      The actual sentence is “…there are many manufacturing processes that typically generate non-normally distributed outputs, even when in control. Below is a list of twenty such characteristics:”
      The key point of the discussion that follows the list is that all of the measurements listed are bounded by some physical limit and that usually when a process is improved the average of the output distribution is pushed closer to the bound.  Moving the process average closer to the bound tends to make the output distribution skewed.
      This also means that if you are far enough away from the physical limit your data has the chance of passing a test of normality.  We had a discussion about a week ago on this same issue concerning tensile strength.

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