I'm working through some control chart practice problems for the CQT. In one of the problems I worked, 3sigma was equal to A2*Rbar.... this was used to calculate a value of sigma. I understand how that works.

On another problem, it asked for the 3sigma limits given xdoublebar, rbar, and n. So.... I calculate this using the USL and LCL for average and range charts, thinking that the 3sigma limits is the same as the USL-LCL. I look in the solution manual to check my answer and it is wrong... :mad: They used Rbar/d2 to calculate sigma, multiplied it by 3, then added and subtracted it from Xdoublebar to get the answer. The solution manual specifically states that in this problem, it is not asking for the control limits.

So, when is 3sigma equal to Rbar/d2 and when is it equal to A2*Rbar? In other words when is 3sigma equal to the limits and when is it not? :( Does it have anything to do with the difference between the difference between specification limits and upper and lower control limits? If yes, what exactly is the difference between these two?

So, when is 3sigma equal to Rbar/d2 and when is it equal to A2*Rbar? In other words when is 3sigma equal to the limits and when is it not? :( Does it have anything to do with the difference between the difference between specification limits and upper and lower control limits? If yes, what exactly is the difference between these two?

I think it would be helpful for you to post the specific details of the problem in question so that someone can help you sort it out. In the quoted passage above you use the phrase "difference between" three times (once in error?) and it's hard to tell what you're asking. At the risk of adding to the confusion, and without knowing your own level of training in control charts, I can say that there is no inherent relationship between control limits and specification limits; in order to calculate control limits you don't need to know what the specification limits are, or even if there is a specification.

I echo that. Control charts are aimed at the "process" more than at the finished product. We just use measurements of characteristics on the product to help determine if the process is in control, not whether the product meets the specs.

Different processes have different capabilities. We can turn a shaft in a fifty-year-old Brown & Sharpe lathe or in a brand new CNC Swiss turning center.

The B&S might be lucky to hold the process to plus or minus one thousandth of an inch, the Swiss can routinely hold target diameter to plus or minus fifty millionths of an inch. Neither has anything to do with tolerance of the part, itself, except in choosing which process is most cost effective in producing the part you need to the tolerances required for form, fit, function.

just the same
So, when is 3sigma equal to Rbar/d2 and when is it equal to A2*Rbar? In other words when is 3sigma equal to the limits and when is it not? :( Does it have anything to do with the difference between the difference between specification limits and upper and lower control limits? If yes, what exactly is the difference between these two?

A2 = 3/d2/Subgroup_Size^0.5
ds3_within =A2* Rbar (3 times the ds_within; ds_within = Rbar/d2/Subgroup_Size^0.5)

UCL = Average + ds3_within
LCL = Average - ds3_within

and as Wes said, nothing to do with specs. :lol: