4. Wonder Shed Inc. is a manufacturer of storage sheds. The manufacturing proces
ID: 355515 • Letter: 4
Question
4. Wonder Shed Inc. is a manufacturer of storage sheds. The manufacturing process involves the procurement of sheets of steel that will be used to form both the roof and the base of each shed.
The first step involves separating the material need for the roof from that needed for the base. Then the roof and the base can be fabricated in parallel, or simultaneously. Roof fabrication involves first punching and then forming the roof to shape. Base fabrication entails the punching-and-forming process plus a subassembly operation.
Fabricated roofs and bases are then assembled into finished sheds that are subsequently inspected for quality assurance. A list of activities needed to fabricate a roof, fabricate a base, and assemble a shed is given in Table 4.1. A flowchart of the process is shown in Figure 4.1.
4.1 (1 point) We use a beta distribution to represent an activity duration. (Note that it is a BETA DISTRIBUTION.) We assume that the activity durations are independent. We denote the optimistic, the most likely and the pessimistic times by a, c and b. Calculate the mean time and the variance of each activity duration and fill in the blanks of the table below.
Activity
a
c
b
Mean
Variance
1
5
10
20
2
15
20
35
3
10
20
25
4
5
7
10
5
5
10
20
6
10
20
30
7
10
12
15
8
15
30
40
4.2. (1 point) The process contains two paths:
Path 1 : Start ? 1 ? 3 ? 5 ? 7 ? 8 ? End
Path 2 : Start ? 1 ? 2 ? 4 ? 6 ? 7 ? 8 ? End
What are the mean and the variance of the duration of each path? Fill in the following table.
Mean
Variance
Path 1
Path 2
4.3. (2 points) Based on Central Limit Theorem, we assume that the duration of each path is normally distributed with mean and variance given in 4.2. We also assume that the durations of the two paths are independent random variables. What is the probability that both paths are completed within 110 minutes?
4.4. (2 points) Based on Central Limit Theorem, we assume that the duration of each path is normally distributed with mean and variance given in 4.2. We also assume that the durations of the two paths are independent random variables. What is the time T for which the probability to complete the longest path in mean time in 4.2 is 99%?
Activity
a
c
b
Mean
Variance
1
5
10
20
2
15
20
35
3
10
20
25
4
5
7
10
5
5
10
20
6
10
20
30
7
10
12
15
8
15
30
40
InputStart 1 7-8 (End)+ Output 2 4 FIGURE 4.1 Process Flowchart for Wonder Shed Inc.Explanation / Answer
Please find below answer to question 4.1 :
Following formula to be noted :
Accordingly the filled up table with mean time and variance as follows :
Activity
A
c
B
Mean ( rounded to 2 decimal places )
Variance ( rounded to 2 decimal places )
1
5
10
20
10.83
6.25
2
15
20
35
21.67
11.11
3
10
20
25
19.17
6.25
4
5
7
10
7.17
0.69
5
5
10
20
10.83
6.25
6
10
20
30
20
11.11
7
10
12
15
12.17
0.69
8
15
30
40
29.17
17.36
Activity
A
c
B
Mean ( rounded to 2 decimal places )
Variance ( rounded to 2 decimal places )
1
5
10
20
10.83
6.25
2
15
20
35
21.67
11.11
3
10
20
25
19.17
6.25
4
5
7
10
7.17
0.69
5
5
10
20
10.83
6.25
6
10
20
30
20
11.11
7
10
12
15
12.17
0.69
8
15
30
40
29.17
17.36
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