XBar-S A3, B3 and B4 where n>25

[Inspector-71]

I find myself having to produce control charts in excel to interact with our datalogger. So I need to calculate control limits manually for an X-Bar S charts. Unfortunately, the subgroup size will be 60 (readings every 0.5 secs average over 30 secs for up to 4 hours) and I can’t find any reference for she appropriate Shewhart constants for such a high subgroup size. Everything I can find ends at n=25.

Do they exist or is n=25 considered the maximum?

Thanks

 

[Bill McNeese]

You can use values of C4 to calculate the control chart constants for the Xbar-s control chart as follows:

A3=3/(c4*sqrt)

B3 = 1-(3/c4)*sqrt(1-(c4)^2))

B4 = 1+(3/c4)*sqrt(1-(c4)^2))


The values of c4 require the use of gamma function, which is in Excel 2013 but no earlier versions (not sure about Excel 2010). The formula for c4 can be found here:

http://v8doc.sas.com/sashtml/qc/chapc/sect7.htm

The attached workbook has the c4 values up to 100 along with the values of A3, B3 and B4.

That being said, please remember rational subgrouping. You want to subgroup your data so that you explore the variation of interest to you on the Xbar chart and on the R chart. Taking data as it comes may not lead to rational subgrouping.

 

[Inspector-71]

Thanks for the info. Much appreciated

 

[ExcelGuy]

Please note that there is an error in the above attached worksheet. B3 is calculated incorrectly.

An If statement is used to return a blank for n values 2,3,4, and 5: The first part of the argument uses the correct equation for B3 when doing the logical check, but the value calculation incorrectly adds to 1 rather than subtracts from 1.
No biggie but it threw me for a loop.

 

[Bill McNeese]

Thanks for seeing it. Kind of obvious when B3 = B4 but i didn't notice that years ago. Corrected workbook is attached.