Given below are the values of the sample mean (X bar) and the range (R) for ten samples of size 5 each.

Question

Given below are the values of the sample mean ( \(\overline{X}\)) and the range (R) for ten samples of size 5 each. Find the control charts and comment on the state of the process.

Sample number	1	2	3	4	5	6	7	8	9	10
Mean (\(\overline{X}\))	43	49	37	44	45	37	51	46	43	47
Range (R)	5	6	5	7	7	4	8	6	4	6

Use A₂ = 0.58, D₃ = 0, D₄ = 2.115

Answer 1

We observe that all the sample range values are within the control limits values of R chart, But two values of the sample \(\overline{X}\) (i.e) 37, 37 lies below the LCL and 49, 51 lie above the UCL. So the statistical process is out of control.