A circuit board manufacturing line is under investigation because one partic- ular solder joint connection has demonstrated failures in the field. It has been decided to construct control charts to study the process. 40 samples of size 4 of circuit boards have been collected from the process and for each board the solder joint of interest is assessed; a composite score is determined for the joint that reflects such characteristics as joint coverage, finish, and deposited solder geometry. The composite score data for the solder joints is shown in the table. Sample X1 X2 X3 X4 Sample X1 X2 X3 X4
1 16.4 22.2 16.7 19.7 21 17.6 16.4 17.3 17.7
2 16.2 19.6 19.7 19.6 22 19.1 18.1 15.3 15.2
3 15.7 17.2 21.4 22.1 23 14.9 17.8 16.3 17.6
4 17.4 15.9 20.3 16.8 2417.6 14.3 17.4 15.9
5 17 16.2 21.5 20.4 25 18.1 13.1 15.8 15.9
6 16.8 17.6 16 18.8 26 16.6 21.5 18 16
7 18.9 18.1 20.3 18.6 27 19.6 18.7 16.3 17.3
8 16.2 15.5 18.7 20.2 28 16.2 19 19.3 19.8
9 16 15.4 14 19.4 29 21.4 22.8 19.3 12.5
10 19.8 15.7 16.8 20.3 30 21 18.7 18.1 16.9
11 21.4 19.1 14.8 16.6 31 17.1 18.9 22 17.2
12 17.8 22.8 20.8 19.8 32 13.2 17.8 18.8 17.4
13 20.2 15.7 17.5 15.5 33 19.7 21.6 17.4 16.8
14 15.4 19.1 18.1 17.5 34 17.3 16 21.5 18.3
15 16 18.8 15.9 21.5 35 19.7 19.8 17.9 21.5
16 17.9 17 20.4 19.1 36 17.2 18.7 18.4 19.6
17 16.7 18.4 16.5 19.9 37 16.1 15.3 19.5 16.5
18 20.9 19.4 21.4 18.2 38 19.3 18.8 18.5 18.6
19 1 7.6 16.8 20.3 18.4 39 18.8 14.7 18.2 17.7
20 16.1 18.9 16.2 18.6 40 19.3 15.2 20.7 20.4
(a) Construct X and R control charts. Is the process in control? Why or why not? Clearly identify all rule violations, if any.
(b) Construct X and control charts.