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Control Chart and Process Stability

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  • #32667

    Alee
    Participant

    Hi All,
       I have one doubt.
       If the process data are not normal distributed, can we use control chart to measure its stability?
        If can not, how can we measure the stability of a process whose data are not normal distributed.
     
     

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    #87508

    Mike Smith
    Participant

    Alee
    The data for a control chart does not have to be normal.
    As Dr. Donald Wheeler says in his book Understanding Variation, SPC Press, (p24)(He uses process behavior chart instead of the term control chart):
    By characterizing the extent of routine variation, the limits on a process behavior chart allow you to differentiate between routine variation and exceptional variation. If, over a reasonably long time, all of the points fall within the limitsof a process behavior chart, and if the points are well-behaved, then the process can be said to display nothing but routine variation. When this happens the process can be thought of as being predictable within those limits, and it is reasonable to expect that, unless something is changed, it will continue to operate this way in the future.Thus, the limits on a process behavior chart allow you to characterize the behavior of your process as predictable or unpredictable, and define how much routine variation you should expect in the future.

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    #87521

    Gabriel
    Participant

    Absolutely yes. You can. Stability = same distribution over the time and has nothing to do with normality. If you use Xbar with a respectable subgroup size, the Xbar distribution will be pretty normal even if the process distribution is not (because of the central limit theorem). If the variable you are charted is VERY skewed (for examples, iX (individuals), Xbar with very small subgroups such as 2) you can still try to use the control charts with the typical calculation of the control limits. In the worst case, if you find problems (for example, too frequently you find points outside the control limit to the side of the long tail of the skewed distribution, but never find an assignable cause) you can change the method of calculating the control limits (for example, you can use the percentiles method or you can “normalize” the distribution via a transformation). But only if needed. Think that R, S, p, np and other variables frequently charted are never normally distributed, and yet the control limits are calculated at ±3 sigmas as you would do for a normal distribution. I never heard of someone who “normalized” the ranges distribution, for example.
    Dr. Deming’s comment on this subject: “What Normal distribution?”

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