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Bayfield Mud Company case. In their text Quantitative
Chapter 13, Problem 89SE(choose chapter or problem)
Problem 89SE
Bayfield Mud Company case. In their text Quantitative Analysis of Management (2005), B. Render (Rollins College) and R. M. Stair (Florida State University) present the case of the Bayfield Mud Company. Bayfield supplies boxcars of 50-pound bags of mud treating agents to the Wet-Land Drilling Company. Mud treating agents are used to control the pH and other chemical properties of the cone during oil drilling operations. Wet-Land has complained to Bayfield that its most recent shipment of bags were underweight by about 5%. (The use of underweight bags may result in poor chemical control during drilling, which may hurt drilling efficiency, resulting in serious economic consequences.) Afraid of losing a longtime customer, Bayfield immediately began investigating their production process. Management suspected that the causes of the problem were the recently added third shift and the fact that all three shifts were under pressure to increase output to meet increasing demand for the product. Their quality-control staff began randomly sampling and weighing six bags of output each hour. The average weight of each sample over the last 3 days is recorded in the table below along with the weight of the heaviest and lightest bags in each sample. Does it appear that management’s suspicion about the third shift is correct? Explain?
Questions & Answers
QUESTION:
Problem 89SE
Bayfield Mud Company case. In their text Quantitative Analysis of Management (2005), B. Render (Rollins College) and R. M. Stair (Florida State University) present the case of the Bayfield Mud Company. Bayfield supplies boxcars of 50-pound bags of mud treating agents to the Wet-Land Drilling Company. Mud treating agents are used to control the pH and other chemical properties of the cone during oil drilling operations. Wet-Land has complained to Bayfield that its most recent shipment of bags were underweight by about 5%. (The use of underweight bags may result in poor chemical control during drilling, which may hurt drilling efficiency, resulting in serious economic consequences.) Afraid of losing a longtime customer, Bayfield immediately began investigating their production process. Management suspected that the causes of the problem were the recently added third shift and the fact that all three shifts were under pressure to increase output to meet increasing demand for the product. Their quality-control staff began randomly sampling and weighing six bags of output each hour. The average weight of each sample over the last 3 days is recorded in the table below along with the weight of the heaviest and lightest bags in each sample. Does it appear that management’s suspicion about the third shift is correct? Explain?
ANSWER:
Step 1 of 12
Compute the range for each observation.
TIME |
AVEWT |
LOWWT |
HIGHWT |
HOUR |
Minimum |
Maximum |
Range |
6 |
49.6 |
48.7 |
50.7 |
1 |
48.7 |
50.7 |
2 |
7 |
50.2 |
49.1 |
51.2 |
2 |
49.1 |
51.2 |
2.1 |
8 |
50.6 |
49.6 |
51.4 |
3 |
49.6 |
51.4 |
1.8 |
9 |
50.8 |
50.2 |
51.8 |
4 |
50.2 |
51.8 |
1.6 |
10 |
49.9 |
49.2 |
52.3 |
5 |
49.2 |
52.3 |
3.1 |
11 |
50.3 |
48.6 |
51.7 |
6 |
48.6 |
51.7 |
3.1 |
12 |
48.6 |
46.2 |
50.4 |
7 |
46.2 |
50.4 |
4.2 |
1 |
49 |
46.4 |
50 |
8 |
46.4 |
50 |
3.6 |
2 |
49 |
46 |
50.6 |
9 |
46 |
50.6 |
4.6 |
3 |
49.8 |
48.2 |
50.8 |
10 |
48.2 |
50.8 |
2.6 |
4 |
50.3 |
49.2 |
52.7 |
11 |
49.2 |
52.7 |
3.5 |
5 |
51.4 |
50 |
55.3 |
12 |
50 |
55.3 |
5.3 |
6 |
51.6 |
49.2 |
54.7 |
13 |
49.2 |
54.7 |
5.5 |
7 |
51.8 |
50 |
55.6 |
14 |
50 |
55.6 |
5.6 |
8 |
51 |
48.6 |
53.2 |
15 |
48.6 |
53.2 |
4.6 |
9 |
50.5 |
49.4 |
52.4 |
16 |
49.4 |
52.4 |
3 |
10 |
49.2 |
46.1 |
50.7 |
17 |
46.1 |
50.7 |
4.6 |
11 |
49 |
46.3 |
50.8 |
18 |
46.3 |
50.8 |
4.5 |
12 |
48.4 |
45.4 |
50.2 |
19 |
45.4 |
50.2 |
4.8 |
1 |
47.6 |
44.3 |
49.7 |
20 |
44.3 |
49.7 |
5.4 |
2 |
47.4 |
44.1 |
49.6 |
21 |
44.1 |
49.6 |
5.5 |
3 |
48.2 |
45.2 |
49 |
22 |
45.2 |
49 |
3.8 |
4 |
48 |
45.5 |
49.1 |
23 |
45.5 |
49.1 |
3.6 |
5 |
48.4 |
47.1 |
49.6 |
24 |
47.1 |
49.6 |
2.5 |
6 |
48.6 |
47.4 |
52 |
25 |
47.4 |
52 |
4.6 |
7 |
50 |
49.2 |
52.2 |
26 |
49.2 |
52.2 |
3 |
8 |
49.8 |
49 |
52.4 |
27 |
49 |
52.4 |
3.4 |
9 |
50.3 |
49.4 |
51.7 |
28 |
49.4 |
51.7 |
2.3 |
10 |
50.2 |
49.6 |
51.8 |
29 |
49.6 |
51.8 |
2.2 |
11 |
50 |
49 |
52.3 |
30 |
49 |
52.3 |
3.3 |
12 |
50 |
48.8 |
52.4 |
31 |
48.8 |
52.4 |
3.6 |
1 |
50.1 |
49.4 |
53.6 |
32 |
49.4 |
53.6 |
4.2 |
2 |
49.7 |
48.6 |
51 |
33 |
48.6 |
51 |
2.4 |
3 |
48.4 |
47.2 |
51.7 |
34 |
47.2 |
51.7 |
4.5 |
4 |
47.2 |
45.3 |
50.9 |
35 |
45.3 |
50.9 |
5.6 |
5 |
46.8 |
44.1 |
49 |
36 |
44.1 |
49 |
4.9 |
6 |
46.8 |
41 |
51.2 |
37 |
41 |
51.2 |
10.2 |
7 |
50 |
46.2 |
51.7 |
38 |
46.2 |
51.7 |
5.5 |
8 |
47.4 |
44 |
48.7 |
39 |
44 |
48.7 |
4.7 |
9 |
47 |
44.2 |
48.9 |
40 |
44.2 |
48.9 |
4.7 |
10 |
47.2 |
46.6 |
50.2 |
41 |
46.6 |
50.2 |
3.6 |
11 |
48.6 |
47 |
50 |
42 |
47 |
50 |
3 |
12 |
49.8 |
48.2 |
50.4 |
43 |
48.2 |
50.4 |
2.2 |
1 |
49.6 |
48.4 |
51.7 |
44 |
48.4 |
51.7 |
3.3 |
2 |
50 |
49 |
52.2 |
45 |
49 |
52.2 |
3.2 |
3 |
50 |
49.2 |
50 |
46 |
49.2 |
50 |
0.8 |
4 |
47.2 |
46.3 |
50.5 |
47 |
46.3 |
50.5 |
4.2 |
5 |
47 |
44.1 |
49.7 |
48 |
44.1 |
49.7 |
5.6 |
6 |
48.4 |
45 |
49 |
49 |
45 |
49 |
4 |
7 |
48.8 |
44.8 |
49.7 |
50 |
44.8 |
49.7 |
4.9 |
8 |
49.6 |
48 |
51.8 |
51 |
48 |
51.8 |
3.8 |
9 |
50 |
48.1 |
52.7 |
52 |
48.1 |
52.7 |
4.6 |
10 |
51 |
48.1 |
55.2 |
53 |
48.1 |
55.2 |
7.1 |
11 |
50.4 |
49.5 |
54.1 |
54 |
49.5 |
54.1 |
4.6 |
12 |
50 |
48.7 |
50.9 |
55 |
48.7 |
50.9 |
2.2 |
1 |
48.9 |
47.6 |
51.2 |
56 |
47.6 |
51.2 |
3.6 |
2 |
49.8 |
48.4 |
51 |
57 |
48.4 |
51 |
2.6 |
3 |
49.8 |
48.8 |
50.8 |
58 |
48.8 |
50.8 |
2 |
4 |
50 |
49.1 |
50.6 |
59 |
49.1 |
50.6 |
1.5 |
5 |
47.8 |
45.2 |
51.2 |
60 |
45.2 |
51.2 |
6 |
6 |
46.4 |
44 |
49.7 |
61 |
44 |
49.7 |
5.7 |
7 |
46.4 |
44.4 |
50 |
62 |
44.4 |
50 |
5.6 |
8 |
47.2 |
46.6 |
48.9 |
63 |
46.6 |
48.9 |
2.3 |
9 |
48.4 |
47.2 |
49.5 |
64 |
47.2 |
49.5 |
2.3 |
10 |
49.2 |
48.1 |
50.7 |
65 |
48.1 |
50.7 |
2.6 |
11 |
48.4 |
47 |
50.8 |
66 |
47 |
50.8 |
3.8 |
12 |
47.2 |
46.4 |
49.2 |
67 |
46.4 |
49.2 |
2.8 |
1 |
47.4 |
46.8 |
49 |
68 |
46.8 |
49 |
2.2 |
2 |
48.8 |
47.2 |
51.4 |
69 |
47.2 |
51.4 |
4.2 |
3 |
49.6 |
49 |
50.6 |
70 |
49 |
50.6 |
1.6 |
4 |
51 |
50.5 |
51.5 |
71 |
50.5 |
51.5 |
1 |
5 |
50.5 |
50 |
51.9 |
72 |
50 |
51.9 |
1.9 |
Table (1)