This should be really simple but I'm getting stuck and I'm probably extremely dumb..
I know that a machine receives two kind of parts:
Type 1 -> with frequency 50 per week, each one is processed for 20 minutes Type 2 -> with frequency 100 per week, each one is processed for 8 minutes
It was told me to consider (in working hours) 1 week = 2400 minutes.
I have to calculate the average arrival rate of the machine and the average service time of the machine.
Average arrival rate of the machine = 50 pieces per week + 100 pieces per week = 150 pieces per week, this is simple since each piece counts as an arrival (they're all equal)
I'm confused with the Average service time per piece of the machine...
I tried:
the machine can serve 2400/20 type 1 pieces per week = 120 and 2400 / 8 type 2 pieces per week = 300
so average_service_rate = (120*50 + 300*100) / 150 = 240, but this is wrong according to my solution (which is 200)...
if I use service times it works: time per each type 1 piece: 20 min time per each type 2 piece: 8 min average_time_per_piece = (20*50 + 8*100)/150 = 12 min, i.e. 12/2400 week so 1/averaget_time_per_piece = average_service_rate = 2400/12 = 200. And this is the right value.
My question is: why my first approach with the average frequency didn't work? What's wrong with it?