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.

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

Question 1: What is the total cost of this system as it is currently set up? Show all calculations

Question 2: (fill out chart at bottom)

Robbins would now like to examine the relative cost-effectiveness of adding one more worker per shift. The new repairperson would be paid $30 per hour, the same rate as before. The cost per breakdown hour is still $75. Stephanie assumes that the repair time with two workers will be exactly one-half the times required with only one repairperson on duty per shift. Thus the new required repair times are as follows:

Table 3
Repair Time Required (hours)	Probability
0.5	0.28
1	0.52
1.5	0.20
Total	1.00

Repeat the simulation on the document below using the revised repair times and circumstances. What is the total cost of this system? Should Stephanie add one more worker per shift or not? Explain and provide complete support for your answer.

two repairpersons

Breakdown Number	RN for Breakdowns	Time between breakdowns	Time of breakdown	Time repairpersons are 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

Q1) The total cost of the system is $208.