The failure rates of 1000 street bulbs in a colony are summarized in the following table.

End of month 1 2 3 4 5 6 Probability of failure to date 0.05 0.20 0.40 0.65 0.85 1.00 The cost of replacing an individual bulb is ! 60. If all the bulbs are replaced simultaneously it would cost Z 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 and replace the individual bulbs when they fail in service during the fixed interval (Group replacement policy).

Find out the optimal replacement policy, i.e. individual replacement policy or group replacement policy? If group replacement policy is optimal, then find at what equal intervals should all the bulbs be replaced?

AppendixLO1