After making several improvements in the east process, you now want to put controls in place to detect new problems if they occur. To help with this, the workers collected a sample of 5 capsules each hour for 42 hours and measured each capsule's CBD contents.

Questions

1. Construct 2 control charts. You can use software to calculate X-bar-bar and S-bar, but you need to show your calculations for UCL and LCL. You may draw the charts by hand or using the software. Excel's line chart feature works well when reformatted: the center line, UCL, and LCL should be straight lines with no dots, whereas the sample measurements should be dots connected with zig-zagging lines (not curves). Alternatively, you can use the control chart options in SPSS.

1. Using just the first 35 samples, calculate X-bar-bar and S-bar. Report these 2 numbers.

2. Construct a X-bar-using-S chart.

a) Calculate the chart's center line, UCL, and LCL.

b) Draw the chart and plot the first 35 data points, i.e., the ones you used to calculate the limits. Was the process in control during that period, or did it go out of control at any time? How do you know? (This is how you validate the chart before workers start using it.)

c) Finally, add the remaining 7 data points on your chart, i.e., the ones you did not use to calculate the limits. Was the process in control throughout that period, or did it go out of control at any time? How do you know?

Sample #	Measurements from 5 capsules per sample
1	20.14	19.88	19.61	19.79	19.08
2	20.34	19.74	20.26	21.11	19.67
3	20.86	21.24	18.69	19.82	20.07
4	19.11	18.77	19.84	20.04	18.76
5	20.05	18.84	20.52	19.89	20.64
6	19.73	18.74	21.23	19.06	19.99
7	20.13	19.83	19.12	19.96	20.75
8	18.88	18.67	20.40	20.27	20.29
9	19.07	20.95	20.52	20.90	20.42
10	19.26	21.37	20.86	20.04	19.17
11	20.00	19.58	18.99	20.49	19.48
12	20.17	21.51	20.46	18.68	21.35
13	18.94	20.08	20.53	20.04	20.44
14	20.10	20.20	19.37	20.90	20.60
15	20.66	19.90	19.27	21.35	20.69
16	20.44	21.58	20.32	20.93	19.85
17	19.94	20.16	20.53	20.68	20.59
18	20.44	19.43	19.41	19.73	20.60
19	20.01	20.54	20.40	21.01	20.38
20	21.35	19.55	20.47	19.34	20.63
21	21.01	20.24	21.32	21.56	20.06
22	19.29	21.53	19.67	20.04	21.24
23	20.26	20.02	19.11	20.26	19.40
24	19.00	20.27	19.60	20.45	18.76
25	19.14	20.02	20.02	18.93	19.71
26	20.11	18.76	20.45	19.64	20.50
27	19.50	21.40	19.63	21.41	19.53
28	21.31	20.16	19.73	19.74	20.01
29	20.12	19.55	19.58	21.48	20.71
30	19.78	19.55	19.78	19.46	19.99
31	18.99	20.53	19.95	19.48	19.66
32	21.30	20.25	20.09	19.99	19.09
33	19.66	19.80	21.17	19.24	21.11
34	19.78	20.03	21.57	19.06	19.69
35	21.15	20.79	21.25	21.22	20.92
36	20.86	19.82	20.38	20.14	19.58
37	20.17	19.86	20.39	21.43	19.90
38	20.58	21.64	21.05	19.19	19.55
39	19.90	21.03	19.25	20.32	20.99
40	20.71	21.76	19.97	19.47	21.69
41	20.86	19.29	21.18	20.54	21.21
42	19.56	19.53	20.43	20.71	20.46