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## Q. 17.1

Parts Delivery System in Automatic Assembly
The cycle time for a given assembly work head = 6 sec. The parts feeder has a feed rate of 50 components per min. The probability that a given component fed by the feeder will pass through the selector is θ = 0.25. The number of parts in the feed track corresponding to the low-level sensor is $n_{f 1} = 6$ . The capacity of the feed track is $n_{f 2} = 18$ parts. Determine (a) how long it will take for the supply of parts in the feed track to go from $n_{f 2}$ to $n_{f1}$ , and (b) how long it will take on average for the supply of parts to go from $n_{f 1}$ to $n_{f 2}$.

## Verified Solution

(a) $T_{c} = 6 sec = 0.1$ min. The rate of depletion of parts in the feed track starting from $n_{f 2}$ will be $R_{c}$= 1/0.1 = 10[/latex parts/min

Time to deplete feed track $(\text{time to go from} n_{f 2}$ to $n_{f 1}) = T_{de} = \frac{18-6}{10}= 1.2$ min

(b) The rate of parts increase in the feed track when the low-level sensor is reached is $fθ – R_{c} = (50)(0.25) – 10 = 12.5 – 10 = 2.5$ parts/min

Time to replenish feed track$(\text{time go from} n_{f 1}$ to $n_{f 2}) = T_{re} = \frac{18-6}{2.5}= 4.8$ min