For any of the control charting questions below, if there are any out-of-control situations (consider all runs-rules described in the instruction), point them out - you need not eliminate any points nor revise the control limits.
1.     For the data set 1, use Minitab and/or MS Excel to do the following (15 points):
a)     Develop the Xbar/R chart - if you use Minitab, also show the "by-hand" calculations for the control limits and center-line. Based on your control chart results, estimate the mean and standard deviation of the process.
b)     Develop the Xbar/s chart and compare this(these) to the Xbar/R chart.
2.     For the data set 2, use Minitab and/or MS Excel to do the following (15 points):
a)     Develop the p-chart (for the control limits and centerline, calculate them by hand)
b)     Develop the np-chart
c)     Develop the q-chart
3.     For the data set 3, use Minitab and/or MS Excel to develop the c-chart . In create the chart, USE ONLY THE FIRST 20 values to develop the limits but plot all 40 plot points on the chart (10 points).
4.     For the data set provided (LSSBB-1-4-Santos - 2021, 4th worksheet), use Minitab and/or MS Excel to develop the u-chart (10 points).
5.     Calculate the probability that an in-control process will yield the Runs Rule violation of having 2 out of 3 consecutive points in the upper "C" zone (i.e., between +2 and +3 sigma control limits)(10 points).
Dataset 1:
Subgp	x1	x2	x3	x4
1	15.0101	15.0099	15.0099	15.0098
2	15.0097	15.0100	15.0100	15.0102
3	15.0100	15.0098	15.0099	15.0101
4	15.0099	15.0101	15.0099	15.0101
5	15.0099	15.0102	15.0100	15.0098
6	15.0100	15.0099	15.0099	15.0099
7	15.0098	15.0100	15.0100	15.0100
8	15.0101	15.0101	15.0100	15.0102
9	15.0099	15.0100	15.0100	15.0100
10	15.0099	15.0100	15.0100	15.0101
11	15.0101	15.0099	15.0101	15.0101
12	15.0101	15.0099	15.0100	15.0100
13	15.0098	15.0099	15.0100	15.0101
14	15.0101	15.0099	15.0102	15.0098
15	15.0101	15.0099	15.0099	15.0101
16	15.0100	15.0100	15.0102	15.0098
17	15.0100	15.0100	15.0100	15.0101
18	15.0099	15.0100	15.0101	15.0100
19	15.0099	15.0100	15.0100	15.0101
20	15.0098	15.0100	15.0099	15.0101
21	15.0101	15.0102	15.0101	15.0100
22	15.0101	15.0100	15.0100	15.0099
23	15.0100	15.0102	15.0100	15.0101
24	15.0102	15.0101	15.0101	15.0099
25	15.0100	15.0101	15.0098	15.0099
26	15.0099	15.0100	15.0099	15.0100
27	15.0100	15.0100	15.0100	15.0101
28	15.0099	15.0100	15.0099	15.0100
29	15.0100	15.0100	15.0099	15.0100
30	15.0099	15.0103	15.0100	15.0100
Dataset 2:
Sample #	# Nonconforming			Sample size for all Sample #'s = 25
1	0
2	1
3	1
4	1
5	0
6	0
7	1
8	0
9	2
10	1
11	1
12	1
13	0
14	0
15	0
16	0
17	1
18	0
19	0
20	1
21	2
22	1
23	0
24	3
25	1
26	0
27	2
28	2
29	3
30	2
Dataset 3:
Sample #	# Defects
1	2
2	7
3	3
4	3
5	6
6	3
7	4
8	3
9	2
10	3
11	5
12	1
13	5
14	2
15	3
16	1
17	4
18	5
19	4
20	5
21	1
22	4
23	4
24	4
25	5
26	3
27	7
28	5
29	2
30	1
31	5
32	2
33	7
34	11
35	8
36	5
37	10
38	3
39	6
40	5
Dataset 4:
Sample #	# Defects		For each Sample #, 5 units were inspected
1	2
2	3
3	10
4	8
5	4
6	2
7	9
8	7
9	9
10	4
11	2
12	7
13	6
14	4
15	4
16	8
17	6
18	4
19	5
20	5
21	7
22	4
23	8
24	5
25	4
26	6
27	6
28	4
29	4
30	5