A transporting company wants to determine its tires replacement policy for their 18 tires-wheeler truck. It is known that tires that fail in service result in significantly higher replacement cost than those replaced before failure. This is due to penalties from the customers due to delays and other overhead costs experienced when the tire fails in service. A tire burst on the road costs $300 per failure. The replacement cost per tire is $75 if all the 18 tires are replaced prior to failure.
The company has done a survey on the probability of tire failure with respect to the number of miles travelled by the truck. The probability of failure is shown in the table below.
|
Period
|
Number of Miles
|
Probability of failure
|
|
1
|
0 - 5,000
|
0.05
|
|
2
|
5,001 - 10,000
|
0.15
|
|
3
|
10,001 - 15,000
|
0.20
|
|
4
|
15,001 - 20,000
|
0.40
|
|
5
|
20,001 - 25,000
|
0.20
|
The tires that fail in a period are replaced in the same period. The company is currently considering two options. First, to determine the optimal replacement age (period) of all tires or second, replace tires as they fail.