# UCL/LCL calculations using Sbar and sigma

#### leaning

##### Involved In Discussions
Hello!

I have an sbar.
So I can calculate the UCL of an s-chart using B4 x sbar, and the LCL using B3 x sbar.

Now, using that same sbar, I can calculate UCL for an Xbar-S chart using Xdbar + A3 x sbar, and the LCL using Xdbar - A3 x Sbar.

OK.
Depending on where I look, sbar is called "standard deviation" or "sigma" (which I don't think is right), because..

There is another formula: UCL = Xdbar + 3 x sigma/sqrt This one uses sigma not s, but it also is referring to standard deviation.

Can anyone help explain how to use sigma vice sbar, and when to use that Xdbar +3 x sigma/sqrt formula?

Regards,
leaning

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
Depending on where I look, sbar is called "standard deviation" or "sigma" (which I don't think is right), because..
Sigma is the name of the Greek letter used to designate the standard deviation, so 'sigma' does refer to the standard deviation. Sbar is just the 'estimate' of the standard deviation. This estimate is calculated as the average standard deviation of several subgroups...they are all equivalent.

There is another formula: UCL = Xdbar + 3 x sigma/sqrt This one uses sigma not s, but it also is referring to standard deviation.

Can anyone help explain how to use sigma vice sbar, and when to use that Xdbar +3 x sigma/sqrt formula?
The formula is the base formula for estimating the within subgroup standard deviation. You should NEVER use this specific formula. The s in this formula is the population standard deviation. It is divided by the square root of the sample size to estimate the variation of the sample averages. A2*Rbar or A3/4*sbar are the correct factors to use in calculating the control limits...

That said, I sense that you are studying for some exam (ASQ CQE?) by trying to remember formulas rather than by first trying to understand the methods and tools of Quality. If you are trying to do this I strongly suggest that you not. True knowledge and ability do not come from passing a test, they come from developing a deep understanding of the subject through study and practice. I suggest that you start with the collected works of Donald Wheeler. His articles are FREE at quality digest and at his SPC Press web site.

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#### leaning

##### Involved In Discussions
Bev D,

Thanks. I'll take a look at what you said.

And FYI, I'm not studying for the exams. I already drove all over the country and took and passed them within a few months of each other: CQT, CQPA, CQIA, CQE, GB, CQI; already had BB). Now, Prometrics does them and so they are more readily available.

I was unemployed, and the local community college saw my resume and hired me part-time to teach a 27-hour cram course to aspiring CQEs to go along with their studies.

The stuff I ask about here on EC are things that aren't clear in my head that I may have muddled through on my own, but once you try to explain that to others, it becomes clear what you know and what you are trying to snow.

So, this isn't for a test for me; it's for my students to know it better than I did.

Thanks for your info and have a good one. Regards,
leaning

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