ABS specializes in repair and maintenance of industrial machines.One repair technician has been assigned to five identical grinding machines for repair and maintenance.The machine breaks down after about 20 hours of use,and breakdowns have a Poisson probability distribution.It takes 6 hours to repair a machine,and repair times follow an exponential distribution.Machine downtime costs the company $250 an hour,and the technician is paid $50 an hour.Determine the average number of machines working if the number of technicians is equal to two.
A)3.72
B)3.21
C)2.32
D)1.32

Question

Quizplus · Accepted Answer

The average number of machines working can be calculated using the formula for the effective operational availability of the machines, considering the Poisson and exponential distributions for breakdowns and repairs, respectively. Given two technicians, each capable of repairing a machine in 6 hours, and machines that break down on average after 20 hours of operation, the system's dynamics can be modeled to find the steady-state number of machines operational. The calculation involves understanding the rate of breakdowns versus the rate of repair, which, given the parameters, leads to an average of approximately 3.72 machines being operational over time. This takes into account the repair time, the breakdown rate, and the availability of technicians to perform repairs.

ABS Specializes in Repair and Maintenance of Industrial Machines