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Question

In a machine shop with 100 automatic machining centres, a maintenance technician serves an 8 hour shift. If there is on average 12 machine breakdowns per 24 hours and if a Technician is away from the workshop 1 hour whenever he or she inspects a breakdown, how many technicians are needed on any given shift to have no more than 1% chance of a Breakdown going undetected? Assume breakdowns are detected only from the workshop

Answer 1

If you assume that the breakdowns are independent, then you want to use a Poisson distribution for their occurrence.

If you have N techs on duty, then there will be an undetected breakdown every time there are N+1 breakdowns within a 1-hour period.

You can determine the N for which the probability of this happening is less than 1%.

Take a look at:
http://en.wikipedia.org/wiki/Poisson_distribution