Question

The net weight (in oz.) of a dry bleach product is to be monitored by X ̅ and R and X ̅ and S control charts using a sample size of n = 5. Data for 20 preliminary samples are shown below.

Subgroup Number	X1	X2	X3	X4	X5
1	8	10	11	15	12
2	10	9	16	14	8
3	11	12	10	16	14
4	7	11	8	13	9
5	9	10	12	11	16
6	12	11	10	14	13
7	8	10	13	9	12
8	14	9	8	14	13
9	9	10	13	12	10
10	8	9	10	13	12
11	10	12	14	16	11
12	14	13	9	11	8
13	16	10	12	15	10
14	8	13	10	12	9
15	12	14	8	16	11
16	8	9	10	14	12
17	9	13	12	10	14
18	14	12	10	11	13
19	11	16	9	12	10
20	13	9	12	14	7

a. Determine the trial central line and control limits for the X and R (24 points).

b. Determine the trial central line and control limits for the X and S (24 points).

Answer 1