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X-bar R vs. X-bar S

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  • December 1, 2007 at 12:14 am #48805

    Rainman
    ★ 10 Years ★
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    My understanding of why an X-bar R chart can be better than an X-bar S chart is that at small sample sizes, the range gives a better estimate of the variation than the standard deviation.  At one time I even had a scholarly article that discussed it, but now I can’t find it.  Does anyone have a source for an article on this topic?

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    December 10, 2007 at 3:00 pm #165945

    Jen
    ★ 10 Years ★
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    Rainman,
    A good reference book that I use is Implementing Six Sigma by Forrest W. Breyfogle III.  It is a great reference book.  You are correct, for small sample sizes n<=9 (typically around n = 4 to 6) you would want to use the R value and estimate the standard deviation as Rbar/d2.
    For larger subgroups n>10 the above method is less efficient and so you can move to using the Xbar and s chart where s = [sum(xi-xbar)squared/(n-1)]1/2 power.

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