Answer to Question #79134 in Statistics and Probability for Kennedy

Question

The failure rates of 1000 street bulbs in a town are summarized in the table below:
End of Month
1
2
3
4
5
6
Probability of failure to date
0.05
0.20
0.40
0.65
0.85
1.0
The cost of replacing an individual bulb is Sh. 60. If all the bulbs are replaced simultaneously it would cost Sh. 25 per bulb. Any one of the following two options can be followed to replace the bulbs:-
i. Replace the bulbs individually when they fail (individual replacement policy)
ii. Replace all the bulbs simultaneously at fixed intervals (Group replacement policy)
Find out the optimal replacement policy? If group policy is optimal, find at what equal intervals should all the bulbs be replaced?

Answer 1

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