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  • #48660

    yuwx
    Member

    Hi, All,
    I have a question on the S-chart Center Line. I attached the data in the end of this notes. I input data into Minitab15, chose Control Chart/Xbar-SChart, In the Xbar-S chart Options, I open the Estimate Tab, The Pool Stdandard Variation and Unsing Unbiased Constand are defult selected. But I do not understand how the data come? In this case, the Center Line (Sbar) for S chart is 0.511, but when I use a manual calculaton, considering unbiase constant c4 and pool standard vaitation, I still do not know how Minitab get this number.  Can somebody with extensive statistic knowledge help me? I ask a good MBB in my company but still can not get the answer. Thanks in Advance!! [email protected]
    Subgroup Value1 24.01 25.21 25.51 24.61 24.82 24.92 24.72 24.82 25.12 24.83 25.13 25.03 26.13 24.93 25.94 24.24 25.14 25.14 24.44 25.05 25.05 25.65 24.95 25.15 24.76 24.66 24.16 24.16 25.56 24.67 25.77 25.57 24.27 24.87 25.98 25.88 25.88 25.18 24.98 25.69 24.79 24.69 25.79 25.09 24.210 25.310 24.110 25.610 24.710 25.011 25.011 25.011 24.211 24.911 23.812 24.812 24.512 24.912 25.412 24.813 25.013 25.513 25.413 25.613 24.614 24.114 25.114 25.614 24.614 24.515 23.915 24.615 25.215 24.715 25.416 24.716 25.116 25.016 23.716 25.717 25.917 23.317 24.517 25.517 24.118 25.518 25.218 25.118 25.018 25.419 25.219 24.119 25.319 24.919 24.720 25.020 25.420 24.720 24.820 24.7
     

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    #164734

    Dr. Scott
    Participant

    yuwx,
    It depends on whether you choose the “Sbar” or the “pooled standard deviation” in the “estimate” options in the “Xbar-S Options” menu.
    Regards,
    Dr.Scott 
     
     

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    #164740

    yuwx
    Member

    Thanks Dr Scott:
    Sorry for my confusion. My question is: what kind of formula Minitab used to calculate the Center Line if both Pool Standard Variation and Use Biased Constant are selected? e.g. can somebody show me how to get the number 0.511 manually using excel? I do not have problem to get a number like 0.505 and 5.34 manually. I just do not know to get the number like Minitab turn out.
    Pretty chanllenging…:-)
    Thanks,
     

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    #164763

    BC
    Participant

    yuwx,
    I get the following in Excel:

    0.54171

     pooled sd

    0.505066
     avg sd

    0.513102

     raw sd
    “Raw sd” means the simple standard deviation of the 100 data points.  No combination that I know of gives 0.511, but like you, I get 0.511 in MTB-15.  When I divide avg sd by C4, I get 0.537.  You might want to contact Minitab directly, at minitab.com.

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    #164776

    Dr. Scott
    Participant

    yuwx,
    I agree with BC that you should contact Minitab on this one. I could not replicate its .511 answer either. Sorry I couldn’t help.
    Please let me know what they say.
    Thanks,
    Dr. Scott
     
     

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    #164798

    Bower Chiel
    Participant

    Hi YuwxThe default estimation method used in Minitab is the pooled standard deviation method with the use of an unbiasing constant. With constant sample size the pooled variance is simply the mean of the variances of the 20 subgroups which I obtained to be 0.2934 giving 0.5417 as the pooled standard deviation. The degrees of freedom for this estimate are 80 – think of 20 subgroups each with 4 degrees of freedom. The process sigma is finally estimated by dividing the pooled standard deviation by the unbiasing constant c4 for 80+1 degrees of freedom giving 0.5417/0.9969 = 0.5434.Now the subtle thing about the s chart is that the mean of the subgroup standard deviation s in the long term is not sigma but c4*sigma. In other words the centre line on the s chart at c4*sigma. c4 is the unbiasing constant for the subgroup size, which is 5 here, and it has value 0.9400. Thus I get 0.9400*0.5417 = 0.511 as the centre line which agrees with Minitab.Minitab explains all this in great detail via the Help button for the s chart. With the Options, Estimate dialog box active click Help > See also > Methods and formulas. Look at methods for estimating standard deviation under Methods and also at centre line under S chart. In the methods section clicking on the underlined word “table” takes you to a table giving values of the unbiasing constant. See also > Methods and formulas. Look at methods for estimating standard deviation under Methods and also at centre line under S chart. In the methods section clicking on the underlined word “table” takes you to a table giving values of the unbiasing constant. See also > Methods and formulas. Look at methods for estimating standard deviation under Methods and also at centre line under S chart. In the methods section clicking on the underlined word “table” takes you to a table giving values of the unbiasing constant. Methods and formulas. Look at methods for estimating standard deviation under Methods and also at centre line under S chart. In the methods section clicking on the underlined word “table” takes you to a table giving values of the unbiasing constant. Methods and formulas. Look at methods for estimating standard deviation under Methods and also at centre line under S chart. In the methods section clicking on the underlined word “table” takes you to a table giving values of the unbiasing constant.Best WishesBower Chiel

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    #164801

    Dr. Scott
    Participant

    Bower Chiel,
    I am not trying to be difficult, but 0.9400*0.5417 = 0.511 is not correct, 0.9400*0.5417 = 0.509 (I know that is just a gnat’s hair away). But it still doesn’t “add” up.
     
    I have used nearly every formula and approach, and like the questioner I have been unable to replicate what Minitab reports.
     
    Regards,
     
    Dr. Scott

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    #164807

    Bower Chiel
    Participant

    Hi AllI do apologise. I should have typed: – “Thus I get 0.9400*0.5434 = 0.511 as the centre line which agrees with Minitab.” 0.5434 is the estimate of sigma obtained in the previous paragraph.Best WishesBower

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    #164808

    yuwx
    Member

    Thank Bower and Dr Scott, great discussion!!!
    here is another way to get a number of 0.511, but I do not know how accurate it is:
    supposed mintab just take Sbar=0.505 as Sp, then unbiasedS=0.505/C4(n+1), in this case, n=20, C4(21)=0.9875, then S=0.511.
    But not sure whether we can do this, but at least Bower’s explaination makes sense. Thanks!

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    #164830

    Dr. Scott
    Participant

    Bower,
    Finally! Way to go and great job helping all of us figure this out. I was overlooking that Minitab automatically uses the bias constant in the subgroup calculation, and then gives you the option of using it in the control chart estimate menu. Now that I use both bias corrections, I get the same answer as Minitab.
    But do me a favor, copy the messages you sent to me and send them directly to yuwx. Otherwise, s/he will not see them unless s/he comes back to the thread to check (s/he will be alerted by email if you send direct). 
    Again, great job and thanks,
    Dr. Scott 

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    #164840

    Ward
    Participant

    Great explanation and appropriate recognition of Minitab’s Help Function. It is absolutely the best help menu of any s/w program I have used. It is rare that I have not found (and quickly) an answer in the Methods and Formula area. I always point students to it, by getting them to discover the answers to the questions they ask me. The benefit is 3-fold.
    1) They knew what I told them was correct
    2) They understand all the info that is available in the help menu
    3) They don’t call me or e-mail me with those types of questions later!Another hint is to choose Help after choosing the tool you are interested in. For this example,
    Stat>Control Charts>Variables Charts for Subgroups>X-bar-S>Help>See Also (top right of help page>Methods & Formulas>Methods>Methods for Estimating Standard Deviation
    It narrows down the search area for the questions you have

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    #165049

    Bower Chiel
    Participant

    Hi Yuwx
     
    Thanks to you (and to Pete and Dr Scott) for your kind comments.
    I don’t think that your alternative suggestion is valid.  I’d stick with the estimation methods described in Minitab Help.
    Best Wishes
    Bower Chiel 

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    #165151

    yuwx
    Member

    Thanks Brower, Dr Scott, and Pete for all your contribution to this discussion, I have been watching this discussion closely. I think my question is clear and I will forward the dicussion to the BB and MBB in my company.
    Great Website! and Great people as well!! Thanks again!
    yuwx

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