A company manufactures a variety of specialist precision components for the engineering industries.

A company manufactures a variety of specialist precision components for the engineering industries. When introducing a new component each one is tested for a period of time in order to establish the failure rate. The failure rate for a particular component has been measured as 3 in
every 200 components tested. From now on, 1 in every 20 components will be tested.
a) How many returns can the company expect in every 2000 of the new component to one decimal place?
If they wish to reduce the number of returns by approximately one third, how many components will they need to test to the nearest whole number?
b) The company has two different specialised machines, A and B, each of which can operate independently at full capacity for 220 hours per month. The unavailability per month of the machines due to faults is 4 hours for Machine A and 10 hours for Machine B. What is the probability of both A and B being unavailable at the same time during a month? If a second machine, of the same type and unavailability as B, is purchased to act as standby for Machine B, what will be the expected number of hours of 'B' production lost per year?
c) Discuss a number of reasons why the calculations in b) might be unrealistic methods of calculating the possibilities of lost production.

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