REPLACEMENT PROBLEM

A factory has two identical machines which must be kept operating at all times. A check on historical records revealed that the failure probabilities of a machine are as shown in the following table.

LIFE (weeks) PROBABILITY

1 .05

2 .20

3 .25

4 .30

5 .15

6 .05

(Thus there is a 5% chance that a machine will last for only one week, a 20% chance that it will last for only two weeks, etc.)

According to the service contract, there are two costs to be paid when a machine is repaired. There is a fee of 200 to be paid to an external service contractor who sends an engineer to fix one or both machines. There is also a charge of 80 per machine for spare parts each time a machine is repaired.

You are asked to compare two replacement policies.

(1) Separate replacement: in this case, a machine is repaired when it breaks down.

(2) Joint replacement: in which both machines are repaired when either of them fails.

What are the factors that may determine the choice of the policies?

For simplicity, assume that machines always fail at the end of a week and are repaired immediately.