The following table gives probability distribution of failures observed for a certain type of light bulbs:

There are 10,000 bulbs in use and it costs Rs. 20 to replace an individual bulb which has burnt out at the end of the week. If all bulbs are replaced simultaneously it would cost Rs. 14 per bulb. It is proposed to replace all bulbs at fixed interval of time, irrespective of their status and to continue replacing burnt out bulbs at the end of every week. At what interval should all the bulbs be replaced? What is the average cost of replacement if all the bulbs are replaced as per individual replacement policy? What is the optimal replacement policy?

Mumbai University > Mechanical Engineering > Sem 7 > Operations Research

Marks: 10 Marks

Year: Dec 2015

Let $p_i$ be the probability that a new light bulb fails during the ith week of its life. Then we get following probability distribution of the lives of the bulb:

$p_1=0.05 \\ p_2=0.10 \\ p_3=0.25 \\ p_4=0.35 \\ p_5=0.25$

Since the sum of all probabilities is unity, all probabilities higher …