Pls Help: CL for Xbar-S chart

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 
 
 

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.

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

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

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 

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