a- Calculate the Range Column in Excel (Largest-Smallest) and find mean and standard deviations for Average Weight, Smallest, Largest, and Range columns.
b- What is the standard deviation of individual bags if sample averages are based on 9 bags? Explain your finding. Hint: σx-bar = σ/sqrt(n). Having σx-bar based on part b calculation, solve for σ given n= 9
c- Does the ADS data support the claim by DCI that the average weight of bags is less than 50 lbs.? Use Alpha=0.01 and do hypothesis testing on mean.
d- Construct a time series plot of all four variables (4 graphs) and discuss your findings based on the graphs.
e- Construct X-bar and R Charts, graph, and discuss your findings based on the control charts. Is it out of control? Why? Explain.
f- Is there any differences between performances of three shifts? Hint: (Carve out the morning, afternoon, and night shift data into three columns and graph them. Explain your findings.
g- Use One Way Analysis of Variance (ANOVA)to compare the three groups (shifts) to test if there is significant differences in the performance of three shifts. Use Alpha =0.01. Can you conclude that night shift is to be blamed for most of the variation?
h- Assume Tolerance limits of 50±1.5 lbs. is specified in the sales contract and find the Process Capability index Cpk. Explain what it indicates and if process is capable to meet contractual agreement.
i- If the improved process average is adjusted to 50.0 lbs. and process standard deviation is reduced to .60, what is the new Cpk? Are you comfortable for making such recommendation to management? Explain.
j- Find the control limits for an X-bar and R chart if a new improved process has average of 50.1 lbs. and R-bar of 2 lbs. Assume n=7 for new process control.
k- Provide complete conclusion regarding your findings and make recommendations regarding the filling process in your conclusion paragraph.
|
Sample #
|
Time
|
Average
|
Smallest
|
Largest
|
|
1
|
6:00 AM
|
49.6
|
48.7
|
50.7
|
|
2
|
7
|
50.2
|
49.1
|
51.2
|
|
3
|
8
|
50.6
|
49.6
|
51.4
|
|
4
|
9
|
50.8
|
50.2
|
51.8
|
|
5
|
10
|
49.9
|
49.2
|
52.3
|
|
6
|
11
|
50.3
|
48.6
|
51.7
|
|
7
|
12 Noon
|
48.6
|
46.2
|
50.4
|
|
8
|
1:00 PM
|
49
|
46.4
|
50
|
|
9
|
2
|
49
|
46
|
50.6
|
|
10
|
3
|
49.8
|
48.2
|
50.8
|
|
11
|
4
|
50.3
|
49.2
|
52.7
|
|
12
|
5
|
51.4
|
50
|
55.3
|
|
13
|
6
|
51.6
|
49.2
|
54.7
|
|
14
|
7
|
51.8
|
50
|
55.6
|
|
15
|
8
|
51
|
48.6
|
53.2
|
|
16
|
9
|
50.5
|
49.4
|
52.4
|
|
17
|
10
|
49.2
|
46.1
|
50.7
|
|
18
|
11
|
49
|
46.3
|
50.8
|
|
19
|
12 Mid Night
|
48.4
|
45.4
|
50.2
|
|
20
|
1:00 AM
|
47.6
|
44.3
|
49.7
|
|
21
|
2
|
47.4
|
44.1
|
49.6
|
|
22
|
3
|
48.2
|
45.2
|
49
|
|
23
|
4
|
48
|
45.5
|
49.1
|
|
24
|
5
|
48.4
|
47.1
|
49.6
|
|
25
|
6
|
48.6
|
47.4
|
52
|
|
26
|
7
|
50
|
49.2
|
52.2
|
|
27
|
8
|
49.8
|
49
|
52.4
|
|
28
|
9
|
50.3
|
49.4
|
51.7
|
|
29
|
10
|
50.2
|
49.6
|
51.8
|
|
30
|
11
|
50
|
49
|
52.3
|
|
31
|
12 Noon
|
50
|
48.8
|
52.4
|
|
32
|
1:00 PM
|
50.1
|
49.4
|
53.6
|
|
33
|
2
|
49.7
|
48.6
|
51
|
|
34
|
3
|
48.4
|
47.2
|
51.7
|
|
35
|
4
|
47.2
|
45.3
|
50.9
|
|
36
|
5
|
46.8
|
44.1
|
49
|
|
37
|
6
|
46.8
|
41
|
51.2
|
|
38
|
7
|
50
|
46.2
|
51.7
|
|
39
|
8
|
47.4
|
44
|
48.7
|
|
40
|
9
|
47
|
44.2
|
48.9
|
|
41
|
10
|
47.2
|
46.6
|
50.2
|
|
42
|
11
|
48.6
|
47
|
50
|
|
43
|
12 Midnight
|
49.8
|
48.2
|
50.4
|
|
44
|
1:00 AM
|
49.6
|
48.4
|
51.7
|
|
45
|
2
|
50
|
49
|
52.2
|
|
46
|
3
|
50
|
49.2
|
50
|
|
47
|
4
|
47.2
|
46.3
|
50.5
|
|
48
|
5
|
47
|
44.1
|
49.7
|
|
49
|
6
|
48.4
|
45
|
49
|
|
50
|
7
|
48.8
|
44.8
|
49.7
|
|
51
|
8
|
49.6
|
48
|
51.8
|
|
52
|
9
|
50
|
48.1
|
52.7
|
|
53
|
10
|
51
|
48.1
|
55.2
|
|
54
|
11
|
50.4
|
49.5
|
54.1
|
|
55
|
12 Noon
|
50
|
48.7
|
50.9
|
|
56
|
1PM
|
48.9
|
47.6
|
51.2
|
|
57
|
2
|
49.8
|
48.4
|
51
|
|
58
|
3
|
49.8
|
48.8
|
50.8
|
|
59
|
4
|
50
|
49.1
|
50.6
|
|
60
|
5
|
47.8
|
45.2
|
51.2
|
|
61
|
6
|
46.4
|
44
|
49.7
|
|
62
|
7
|
46.4
|
44.4
|
50
|
|
63
|
8
|
47.2
|
46.6
|
48.9
|
|
64
|
9
|
48.4
|
47.2
|
49.5
|
|
65
|
10
|
49.2
|
48.1
|
50.7
|
|
66
|
11
|
48.4
|
47
|
50.8
|
|
67
|
12 Midnight
|
47.2
|
46.4
|
49.2
|
|
68
|
1:00 AM
|
47.4
|
46.8
|
49
|
|
69
|
2
|
48.8
|
47.2
|
51.4
|
|
70
|
3
|
49.6
|
49
|
50.6
|
|
71
|
4
|
51
|
50.5
|
51.5
|
|
72
|
5
|
50.5
|
50
|
51.9
|