A chemical plant is being designed with a number of Refiner units, each unit comprising a processor with its own permanently attached Pre-feeder. The Refiner units must be capable of processing a total of 240,000 cubic metres of material per hour and units are availabe in two sizes, 120,000 cubic metres per hour and 60,000 cubic metres per hour. If Refiner breakdowns cause the output to drop below 180,000 cubic metres per hour, it is necessary to shut down the whole manufacturing process.
The exact reliability of the units is unknown but experience suggests that the probability of breakdown in any week should be in the following ranges:
Probability of failure
Pre feeders 0.02-----0.05
There are two possible configurations for the plant, either two 120,000 cubic metre units or four 60,000 cubic metre units.
(1) What is the probability of failure of a two x 120,000 cubic metre unit configuration if .a. units are of poorest quality .b. units are of best quality?
(2) What is the probability of failure of a four x 60,000 cubic metre unit configuration if .a. units are of poorest quality .b. units are of best quality?
By considering best case and worst case scenarios, decide which configuration is better.
Thanks in advance for any help.