The Bedrock Company’s headquarters contains 1000 electric light bulbs. When any bulb fails, it is immediately replaced. From past records of 500 bulbs, the following failures table has been obtained:

Age at failure (months) 2 3 4 5 No. of failed bulbs 100 200 150 50

(i) Calculate the expected number of bulbs to be replaced in each of the first seven months. What rate of failure can be expected in the long run?

(ii) Replacement of individual bulbs costs £0.50 each. What is the average monthly replacement cost? An alternative policy is to replace all the bulbs after a fixed number of months at a cost of £200, as well as replacing any units that fail at the individual price of £0.50 each. Is this preventative maintenance policy justified, and if so, in what month should it come into operation?

(Answer: In order to be consistent, the failures table above must also include month 1 with zero failures. Failures in the first 7 months are 0, 200, 400, 340, 260, 288, and 328. In the long run, the average number of failures per month is 303. The average monthly individual replacement cost is therefore £151.50. The cheapest replacement policy is group replacement every two months at an average monthly cost of £150.)