Question

The AMS technical services team has embarked on a quality improvement effort. Its first project relates to maintaining the target upload speed for its Internet service subscribers. Upload speeds are measured on a device that records the results on a standard scale in which the target value is 1.0. Each day five uploads are randomly selected, and the speed of each upload is measured. The results for 25 days is stored in AMS14.xl

(please provide answers for a through c - THANK YOU!)

a. Construct the appropriate control charts for these data.

b. Is the process in a state of statistical control? Explain.

c. What should the team recommend as the next step to improve the process?

Day   Upload Speed
1   0.96
1   1.01
1   1.12
1   1.07
1   0.97
2   1.06
2   1.00
2   1.02
2   1.16
2   0.96
3   1.00
3   0.90
3   0.98
3   1.18
3   0.96
4   0.92
4   0.89
4   1.01
4   1.16
4   0.90
5   1.02
5   1.16
5   1.03
5   0.89
5   1.00
6   0.88
6   0.92
6   1.03
6   1.16
6   0.91
7   1.05
7   1.13
7   1.01
7   0.93
7   1.03
8   0.95
8   0.86
8   1.14
8   0.90
8   0.95
9   0.99
9   0.89
9   1.00
9   1.15
9   0.92
10   0.89
10   1.18
10   1.03
10   0.96
10   1.04
11   0.97
11   1.13
11   0.95
11   0.86
11   1.06
12   1.00
12   0.87
12   1.02
12   0.98
12   1.13
13   0.96
13   0.79
13   1.17
13   0.97
13   0.95
14   1.03
14   0.89
14   1.03
14   1.12
14   1.03
15   0.96
15   1.12
15   0.95
15   0.88
15   0.99
16   1.01
16   0.87
16   0.99
16   1.04
16   1.16
17   0.98
17   0.85
17   0.99
17   1.04
17   1.16
18   1.03
18   0.82
18   1.21
18   0.98
18   1.08
19   1.02
19   0.84
19   1.15
19   0.94
19   1.08
20   0.90
20   1.02
20   1.10
20   1.04
20   1.08
21   0.96
21   1.05
21   1.01
21   0.93
21   1.01
22   0.89
22   1.04
22   0.97
22   0.99
22   0.95
23   0.96
23   1.00
23   0.97
23   1.04
23   0.95
24   1.01
24   0.98
24   1.04
24   1.01
24   0.92
25   1.01
25   1.00
25   0.92
25   0.90
25   1.11

Answer 1

Below is the table :

						0.2424
# of samples	X_1	X_2	X_3	X_4	X_5	RANGE
1	0.96	1.01	1.12	1.07	0.97	0.16
2	1.06	1	1.02	1.16	0.96	0.2
3	1	0.9	0.98	1.18	0.96	0.28
4	0.92	0.89	1.01	1.16	0.9	0.27
5	1.02	1.16	1.03	0.89	1	0.27
6	0.88	0.92	1.03	1.16	0.91	0.28
7	1.05	1.13	1.01	0.93	1.03	0.2
8	0.95	0.86	1.14	0.9	0.95	0.28
9	0.99	0.89	1	1.15	0.92	0.26
10	0.89	1.18	1.03	0.96	1.04	0.29
11	0.97	1.13	0.95	0.86	1.06	0.27
12	1	0.87	1.02	0.98	1.13	0.26
13	0.96	0.79	1.17	0.97	0.95	0.38
14	1.03	0.89	1.03	1.12	1.03	0.23
15	0.96	1.12	0.95	0.88	0.99	0.24
16	1.01	0.87	0.99	1.04	1.16	0.29
17	0.98	0.85	0.99	1.04	1.16	0.31
18	1.03	0.82	1.21	0.98	1.08	0.39
19	1.02	0.84	1.15	0.94	1.08	0.31
20	0.9	1.02	1.1	1.04	1.08	0.2
21	0.96	1.05	1.01	0.93	1.01	0.12
22	0.89	1.04	0.97	0.99	0.95	0.15
23	0.96	1	0.97	1.04	0.95	0.09
24	1.01	0.98	1.04	1.01	0.92	0.12
25	1.01	1	0.92	0.9	1.11	0.21

TEST 7. 15 points within 1 standard deviation of center line (above and below CL).

Test Failed at points: 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25

C. Since our X bar chart fails in test-7, which shows the stratification pattern failure.

Stratification pattern - pattern is said to be stratification when, majority of points lie near the centre limit and very few near Control limits which suggests the presence of two or more population ( may be different shifts ) - when data from different shifts are combined.

So here we should segregate the data for different shift and then plot the chart.