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Estimation of sigma

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  • #51712

    Lorena
    Participant

    Dear All,
    in my Company the following formula is applied:
    sigma=average moving range/1.128.
    Can you please help me find some material about constant 1.128 and all the hypothesis under which this formula is valid?
    Thannks very much

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    #179991

    Darth
    Participant

    You can estimate the standard deviation using the range with the formula Rbar/d2 where d2 is a constant. The 1.128 is for an assumed sample size of 2. You will see this used in an Individuals control chart for calculating control limits.

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    #179993

    Mikel
    Member

    Wow, pick up a book on SQC and read it.

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    #179996

    Lorena
    Participant

    If you were a little bit clever you would guess that my doubt is that this formula is used improperly, because the situation is quite different from the standard ones discribed in books and I would like to be sure about possible special cases.
    May you find the way not to waste your time like you do.
    Thank you
    Lorena

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    #179998

    Ron
    Member

    Lorena,
    You would be correct in your assumption. That equation is only used in a limited application of a shewhart chart.

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    #180002

    Robert Butler
    Participant

    “In small samples the range and standard deviation are likely to fluctuate together.  If the standard deviation is large, the range is also likely to be large and conversely….If we are interested in analyzing or controlling variability and use small samples, the range may often be employed as a substitute for the standard deviation with little loss of efficiency. In addition to being almost as efficient as the standard deviation in small samples, the range is easy to calculate. 
       Tables of the distribution of the relative range w = R/sigma have been worked out for the normal universe”
      pp. 139 Quality Control and Industrial Statistics 4th Edition – Duncan.
      A check of the table on pp.948 of the above book indicates 1.128 is the value of w in the case of a two sample measure. 
      Why use it?   If your company was or is in a business where the cost per sample is excessive either in terms of time or money or both the use of the equation might have been the only option and, if things haven’t changed, it may still be.

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    #180003

    Mikel
    Member

    I doubt that’s true from your original question.
    May you find a way to help yourself and not get offended when you have not.
    Thank you.

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    #180013

    annon
    Participant

    Hi Robert,
    So based on the included quotation, why go through the calculation for std dev…why not simply use the range when dealing with n=2?  What value is gained in dividing through Rbar with the constant?  Thanks!

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