consider an arrival rate of 50 u/hr to a production line. the units must be processed...

consider an arrival rate of 50 u/hr to a production line. the units must be processed at stations 1 and 2, in that order. station 1 has 2 parallel machines and each unit must spend 30 second at one of the machines. station 2 has 1 machines, with a processing time of 15 seconds, but 75% of the output from station 2 must be reworked to fix quality defects. units may be re-worked multiple times and have a 75% chance of needig mre-work agin each time. what is the utilization of station 2?

Expert Solution

The rate at which units are coming to station 2 after being processed at station 1 are 2 per 30 sec = 1 per 15 sec. or 240 units per hour.

However, as the arrival rate is 50 units per hour, the actual arrival will be 50 units

Out of the 50 units, 75% are re-worked and it goes repetitively

So, number of units worked at station 2 = 50 + 75%*50 + (75%)^2*50 + ...............infinity

= 50*(1/(1-75%)) = 200

The capacity is 15 sec per unit or 60*60/15 = 240 units

Utilization % = Units worked/Capacity*100 = 200/240*100 = 83.33%

keosha answered 2 years ago

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