Question

In a production process, eight samples of size 4 are collected and their means and ranges are given below. Construct a mean chart and range chart with control limits.

Sample number	1	2	3	4	5	6	7	8
\(\overline {X}\)	12	13	11	12	14	13	16	15
R	2	5	4	2	3	2	4	3

Answer 1

Sample number	1	2	3	4	5	6	7	8	Total
\(\overline {X}\)	12	13	11	12	14	13	16	15	106
R	2	5	4	2	3	2	4	3	25

From the values of the control limits for \(\overline {X}\), we observe that sample \(\overline {X}\) value 16 is above the UCL. Hence we conclude that the process is out of control.