Question

The Three Hills Power Company provides electricity to a large metropolitan area through a series of almost 200 hydroelectric generators. Management recognizes that even a well-maintained generator will have periodic failures or breakdowns. Energy demands over the past three years have been consistently high and the company is concerned over downtime of generators. It currently employs 4 highly skilled and highly paid ($30 per hour) repairpersons. Each works every fourth 8-hour shift, so there is a repairperson on duty 24 hours a day, seven days a week.

     Breakdown expenses are also very costly. For each hour that one of its generators is down, Three Hills loses approximately $75. This amount is the charge for reserve power that Three Hills must “borrow” from the neighboring utility company.

     Stephanie Robbins has been assigned to simulate maintenance costs. Her objective is to determine the total cost of the system made up of 1) the service maintenance cost and 2) the machine breakdown cost. The time between successive generator breakdowns varies from one-half hour to 3 hours, and is shown in Table 1 below along with the frequency of each time occurring across 100 breakdowns.

Question 1: Fill out below (table 1)

Table 1
Time between machine failures (hours)	Number of times observed (frequency)	Probability	Cumulative Probability	Random Number Interval
0.5	5
1.0	6
1.5	16
2.0	33
2.5	21
3.0	19
Total	100

Table 2
Repair Time Required (hours)	Probability
1	0.28
2	0.52
3	0.20
Total	1.00

Question 2: Complete a simulation of this scenario for 10 generator breakdowns in the table on the next page. You can assume that there is only one repairperson working at a time and that each repairperson works only an 8-hour shift. Thus, when each person is replaced by the next shift, he or she just hands the tools over to the next worker who continues working on the same generator until the job is completed. Also assume that you are starting the analysis at midnight (time 00:00). Table 2 below shows the required repair time.

one repairperson:

Breakdown Number	RN for Breakdowns	Time between breakdowns	Time of breakdown	Time repairperson is free to begin repair	RN for Repair Time	Repair time required	Time Repair ends	Number of Hours Machine Down
1	.57				.07
2	.17				.60
3	.36				.77
4	.72				.49
5	.85				.76
6	.31				.95
7	.44				.51
8	.30				.16
9	.26				.14
10	.09				.85

Answer 1

Sol:

Q1).

The total cost of the system is $208.

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