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An airport is trying to model its airline inspection costs. One of these costs is the time spent out of service. This time is composed of time spent waiting for inspection and time spent actually being inspected. The time between arrivals at the inspection center and the actual inspection time are both random variables with values and probabilities indicated below. Only one airplane at a time can be inspected, and there is a strict first in/first out service policy. The per day cost associated with an airplane being out of service is $1000. Simulate the inspection process for the next 100 airplanes and determine the average inspection cost.
| Time between arrivals (days) | Probability | Inspection time (days) | Probability | |
| 2 | 0.15 | 1 | 0.1 | |
| 3 | 0.25 | 2 | 0.15 | |
| 5 | 0.3 | 3 | 0.25 | |
| 7 | 0.25 | 4 | 0.3 | |
| 11 | 0.05 | 5 | 0.2 |
Expert Answer
| Time between arrivals (days) | Probability | Cumulative probability | Inspection time (days) | Probability | Cumulative Probability |
| 0.00 | 0.00 | ||||
| 2 | 0.15 | 0.15 | 1 | 0.10 | 0.10 |
| 3 | 0.25 | 0.40 | 2 | 0.15 | 0.25 |
| 5 | 0.30 | 0.70 | 3 | 0.25 | 0.50 |
| 7 | 0.25 | 0.95 | 4 | 0.30 | 0.80 |
| 11 | 0.05 | 1.00 | 5 | 0.20 | 1.00 |
Average time spent waiting for inspection and being inspected = 4.17
Average inspection cost = $4170
| Airplane | Arrival time | Inspection start time | Inspection time | Inspection end time | Total time in system |
| 1 | 7 | 7 | 3 | 10 | 3 |
| 2 | 12 | 12 | 2 | 14 | 2 |
| 3 | 19 | 19 | 4 | 23 | 4 |
| 4 | 26 | 26 | 4 | 30 | 4 |
| 5 | 33 | 33 | 2 | 35 | 2 |
| 6 | 36 | 36 | 4 | 40 | 4 |
| 7 | 47 | 47 | 1 | 48 | 1 |
| 8 | 50 | 50 | 4 | 54 | 4 |
| 9 | 53 | 54 | 3 | 57 | 4 |
| 10 | 55 | 57 | 2 | 59 | 4 |
| 11 | 60 | 60 | 3 | 63 | 3 |
| 12 | 65 | 65 | 4 | 69 | 4 |
Excel sheet attached for 100 iterations.
