Question

Given the following sample data, what would be the Upper and Lower +/- 3 Sigma Control Limits for the corresponding X-bar chart?

Sample	Obs X1	Obs X2	Obs X3	Obs X4	Obs X5	Obs X6
1	36	20	32	28	21	40
2	31	38	35	38	33	32
3	33	28	36	31	25	25
4	38	25	32	40	29	39
5	38	30	28	30	31	31

Answer 1

Sample	Obs X1	Obs X2	Obs X3	Obs X4	Obs X5	Obs X6	average	range
1	36	20	32	28	21	40	29.5000	20.0000
2	31	38	35	38	33	32	34.5000	7.0000
3	33	28	36	31	25	25	29.6667	11.0000
4	38	25	32	40	29	39	33.8333	15.0000
5	38	30	28	30	31	31	31.3333	10.0000
						average	31.7667	12.6000

sample mean x̅ =			31.767
average range R̅ =			12.6000
sample size n   =			6
for sample size n=6, criitcal value of constant A2=					0.483
control line (CL) = x̅=			31.767
upper control limit =x̅+3*A2R̅ =			37.852
lower control limit =x̅-3*A2R̅ =			25.681