9.1- Use the chi-square goodness-off-fit test and a significance level of 0.1 to test the set of interarrival times in Table 9.32 for possible fit to the exponential distribution.
TABLE 9.,3 2
Interarrival times for Exercise 9.1
| 1.9 |
5.3 |
1.1 |
4.7 |
17.8 |
44.3 |
| 9 |
18.9 |
114.2 |
47.3 |
47.1 |
11.2 |
| 60.1 |
38.6 |
107.6 |
56.4 |
10 |
31.4 |
| 58.6 |
5.5 |
11.8 |
62.4 |
24.4 |
0.9 |
| 44.5 |
115.8 |
2 |
5.03 |
21.1 |
2.6 |
9.5- Apply the KS test to the data in Exercise 9.1.
Process Modeling and Analysis in an Assembly Factory
The LeedsSim factory is a traditional assembly facility working as a subcontractor to the telecommunications industry. Their main product is a specialized switchboard cabinet used in the fourth-generation (4G) network base stations. The company has been successful on the sales side, and with the AG expansion taking off, the orders are piling up. Unfortunately, the operations department has had some problems with reaching the desired (and necessary) productivity levels. Therefore, they have decided to seek help to create a simulation model process as a step to analyze and improve the process design.
To find the right level of detail in the model description, they want to start with a simple model and then successively add more details until a suitable model with the right level of complexity is obtained. The simulation should be run over a 3 month (12 week) period of five 8 h workdays/week. A schematic flowchart of the manufacturing process is shown in Figure 9.35.
After the cabinets are completed and inspected, the finished cabinets leave the factory. It is noteworthy that each workstation can handle only one item at a time. Moreover, a forklift truck is required to move the assembled cabinets. Workstations 1 through 3 cannot store items. Similarly, there is no room to store items before workstations 4, but after it, there is room to store two assembled cabinets. At workstation 5, there is ample space to store cabinets before the workstation, but after it, there is only room to store at most two painted cabinets. At the inspection station, there is space to store cabinets both before and after the station.
Table 9.18
Estimated Processing and Inspection Times
| Processing Unit |
Processing Time Distribution |
Parameter Values(h) |
| Workstation 1 |
triangular |
Max = 3, min = 1.5, most likely = 2 |
| Workstation 2 |
triangular |
Max = 3, min = 1.5, most likely = 2 |
| Workstation 3 |
triangular |
Max = 3, min = 1.5, most likely = 2 |
| Workstation 4 |
triangular |
Max = 4, min = 2, most likely = 3 |
| Workstation 5 |
triangular |
Max = 6, min = 3, most likely = 4 |
Each cabinet that is made requires one unit each of five different components/raw materials delivered to the inbound storage area. Workstation 1 requires one unit each of raw materials 1 and 2, workstation 2 requires one unit of raw material 3, and workstation 3 requires one unit each of raw materials 4 and 5. Table 9.18 specifies the estimated processing times in workstations 1 through 5. Table 9.19 shows collected inspection time data that have not it been analyzed. This needs to be done in order to build a valid model of the process.
The performance measure that LeedsSim is must interested in is the number of cabinets produced in a 3 month period. However they also want to keep track of the following:
• The WIP levels (measured in units of raw material)-the total as well as at different parts of the workshop (the mean and the standard deviation for a single run and the mar with 95% confidence intervals in case of multiple simulation runs)
• The inbound storage levels of the raw materials (the maximum, the mean,. and the standard deviation for a single run and the mean with 95% confidence intervals in case of multiple simulation runs)
• The cycle time, measured from the instant a component arrives to the storage area until a finished cabinet leaves the factory (the mean and the standard deviation for a single run and the mean with 95% ) confidence intervals in case of multiple simulation runs) (Hint.: Note that all components for a particular cabinet have the same cycle time.)
Utilizations of workstations and equipment such as the forklift truck (the mean wit h 95% confidence intervals in case of multiple simulation runs)
Table 9.19
Observed Inspection Time Data in Minutes
|
No.
|
Inspection Time
|
No.
|
Inspection Time
|
No.
|
Inspection Time
|
No.
|
Inspection Time
|
|
1
|
0.944
|
31
|
0.21 Pl.
|
61
|
0.313
|
91
|
l.532
|
|
2
|
3.08.4
|
32
|
1_49K
|
62
|
2.12'14
|
92
|
2.561
|
|
3
|
0.169
|
33
|
.7._43
|
|
0.756
|
93
|
6.1%5
|
|
4
|
7,078
|
34
|
1,491
|
64
|
0,991
|
94
|
1.663
|
|
5
|
2.440
|
35
|
0.008.
|
65
|
1.001
|
95
|
0.9914
|
|
6
|
5.A6
|
36
|
0,502
|
66
|
2.070
|
96
|
0,153
|
|
7
|
0.201
|
37
|
2,324
|
67
|
3.216
|
477
|
13135
|
|
8
|
1.185
|
34
|
0.4584
|
68
|
2.037
|
915
|
0.212
|
|
9
|
5.308
|
39
|
1.474
|
69
|
5.358
|
99
|
0_757
|
|
10
|
0.989
|
40
|
1_18.0
|
70
|
0.024
|
100
|
1191
|
|
11
|
0.5W
|
41
|
4.307
|
71
|
2.397
|
101
|
0.063
|
|
12
|
8.176
|
42
|
5.252
|
72
|
4.718
|
102
|
3.571
|
|
13
|
3.676
|
43
|
6.797
|
73
|
1.478
|
103
|
7.869
|
|
14
|
0.504
|
44
|
3 461
|
74
|
1.0843
|
104
|
0_233
|
|
15
|
0.016
|
45
|
0_41E1
|
75
|
12.196
|
105
|
0.661
|
|
16
|
1.392
|
46
|
0.699
|
76
|
0.109
|
106
|
0.697
|
|
17
|
0.552
|
17
|
0293
|
77
|
4.355
|
107
|
4..437
|
|
18
|
2.03
|
48
|
4.245
|
743
|
1.158
|
11-16
|
[P.1345
|
|
19
|
2,&iN
|
444
|
1,594
|
79
|
0.003
|
109
|
1.239
|
|
20
|
5,982
|
.-.47
|
ia,r33
|
mo
|
U.137
|
110
|
0,357
|
|
2]
|
2.337
|
1.1
|
0,381.1
|
81
|
0.293
|
111
|
] .143
|
|
22
|
2.426
|
52
|
1.11C8
|
H2
|
0.193
|
112
|
3.0611
|
|
23
|
0,252
|
53
|
1,457
|
83
|
1.263
|
113
|
0.5.48
|
|
24
|
0.294)
|
54
|
0.206
|
84
|
2.249
|
114
|
3.460
|
|
25
|
5139
|
55
|
0_755
|
85
|
0.6E9
|
115
|
1171
|
|
26
|
1.727
|
56
|
1.786
|
86
|
2.376
|
116
|
3.4o1
|
|
27
|
3.1359
|
57
|
0_510
|
87
|
0.729
|
117
|
3.0132
|
|
28
|
3.356
|
58
|
3.400
|
88
|
1.408
|
118
|
0357
|
|
19
|
13.884
|
59
|
1.6-913
|
89
|
5.199
|
119
|
1098
|
|
30
|
1.992
|
60
|
2.186
|
90
|
3286
|
120
|
0.728
|
Questions
1. The raw material arrives by truck once every week on Monday morning. Each shipment contains 15 units each of the five necessary components, The internal logistics within the factory is such that the transportation time for the incomplete Cabinets can be neglected. However, to transport the assembled cabinet to and from the paint shop, a special type of Forklift truck is needed. The transportation time from the assembly line to the paint shop is exponentially distributed with a mean of 45 min. The transportation time between the paint shop and the inspection station of the loading, dock is normally distributed with a mean of 60 min and a standard deviation of 15 min. After each delivery, the forklift truck always returns to the strategically located parking area to gel new instructions. The travel time for the forklift truck, without between the parking area and each of the workstations is negligible.
Transportation of painted cabinets is prioritized. This means that whenever forklift truck is available for a new assignment (as its parking area), and there are unpainted and painted cabinets awaiting transport, the latter ones will transported first. Currently one forklift truck is available in the factory. For the first model, assume that all painted cabinets pass inspection, so no rework occurs.
a. Analyze the input data for the inspection times and fit a suitable distribution. Build the model and run the simulation once with random seed = 5. How many cabinets are being, produced? How is the WIP situation? What does a plot over the storage inventory levels tell us? Where is the bottleneck?
b. Run the simulation 30 times with different randorn seeds. How many cabinets are being produced on average? What is the standard deviation? How is the WIP situation? Where is the bottleneck? (Hint: Use the Statistics block in the Value library to collect data and analyze it efficiently. For the number of units produced, use a Mean and Variance block, connect it to the exit block, and check the dialogue options Calculate for Multiple Simulations and use number of inputs-1.)
2. In reality, only 75% of the painted cabinets pass the inspection. If a cabinet fails the inspection, it needs to be transported back to the paint shop to be repainted. The transportation time is the same as in the opposite direction (normally distributed will a mean of 60 min and a standard deviation of 15 min). The transportation of painted cabinets that has failed inpection back to the paint shop has higher priority than any other transportation assignment. The forklift truck will always go back to the parking area after a completed mission. When arriving to the paint shop, repainting has higher priority than the ordinary paint jobs and follows an exponential distribution with a mean a 2 h. Inspecting the reworked cabinets is no different from inspecting non-reworked cabinets. How does the introduction of these features affects the performance measures?
a. Run the simulation once with random seed = 5. Flow many cabinets are being produced? How is the W1P situation? Where is the bottleneck?
b. Run the simulation 30 times with different random seeds. Flow many cabinets are being produced on average? What is the standard deviation? Flow is the IN' IP situation? Where is the bottleneck?
3. Based on your understanding of the process, suggest a few design changes and try them out. What is your recommendation to LeedsSim regarding how to improve their operations?
4. In this model, collection of statistics data starts at time zero, when the system empty. It would be more accurate to run the system for a warm-up period, say 1 week before starting to collect data. Implement this and set the difference. Does it change your conclusions?