Question

The following data show the values of sample means and the ranges for ten samples of size 4 each. Construct the control chart for mean and range chart and determine whether the process is in control

Sample number	1	2	3	4	5	6	7	8	9	10
\(\overline {X}\)	29	26	37	34	14	45	39	20	34	23
R	39	10	39	17	12	20	05	21	23	15

Answer 1

Sample number	1	2	3	4	5	6	7	8	9	10	Total
\(\overline {X}\)	29	26	37	34	14	45	39	20	34	23	301
R	39	10	39	17	12	20	05	21	23	15	201

From the values of the control limits for \(\overline {X}\), we observe that one sample \(\overline {X}\) value (45) is above the UCL and one sample \(\overline {X}\) value (14) is below the LCL. Hence we conclude that the process is out of control.