If X-bar = 392 and R-bar = 80:

UCL-R = R-bar * 3.27 = 262
LCL-R = 0 (by definition)

UCL-X = X-bar + 2.66 * R-bar = 392 + 2.66 * 80 = 605
UCL-X = X-bar – 2.66 * R-bar = 392 – 2.66 * 80 = 179

mean392 R-BAR 80
UCL 501 UCLR 124
CL 392 CLR 80
LCL 284 LCLR 37

I fear that your advice has drifted from what Donald J. Wheeler recommends.

If you search for his excellent 2010 article “Individual Charts Done Right and Wrong” (QualityDigest.com), he advises that calculating control limits by “Limits for X = average ± 3 * global standard deviation statistic” is, well, “wrong” and “simply nothing more than another way to lie with statistics.”

With or without a PC, that XmR method “should always be the default option for computing limits for individual values.”

SPC relies on robust estimators to separate any signal from the noise, while =stdev(data) all too efficiently jumbles them together. Granted, if we KNEW that the process was free of special causes (signals), then =stdev(data) would be the best estimator of process common cause sigma, but the whole point of using SPC is to determine whether the process has detectable special causes . . .

-Dale

Using Mean and Standard Deviation:
UCL = Process Mean + 3 * (Process Standard Deviation)
LCL = Process Mean – 3 * (Process Standard Deviation)
UCL = 19.6 + 3 * 2.61 = 27.4
LCL = 19.6 – 3 * 2.61 = 11.8

The results are similar, in this case the XmR has a broader “acceptable” range. The XmR was easier to calculate when people didn’t have PCs on their desks.

Strictly speaking, the limits shouldn’t be calculated based on the data being observed. The limits should be computed when the process is deemed stable, then future observations compared to these limits.

I got lost in the calculation of UCL & LCL metioned in post i.e “the mean of the moving range is multiplied by 2.66, then added to and subtracted from the process data mean (this is roughly equivalent to using 3 times the standard deviation of the individual values data). Our Upper and Lower Control Limits (UCL and LCL) are thus 28.1 and 11.1.”