Your production line for manufacturing a certain precision micro-electronics component consists of 2 stations: A (upstream) and B (downstream). Each station consists of a single machine.

By taking actual data, it has been observed that it takes an average of 30 minutes to process a job in Station A, with a standard deviation of 22.5 minutes. Meanwhile, it has been observed that it takes an average of 20 minutes to process a job in Station B, with a standard deviation of 16 minutes.

In addition, the machine in Station A is subjected to random failure. The mean-time-tofailure is 6 hours, the mean-time-to-repair being 1.5 hours with the standard deviation of repair time being 1.5 hours. On the other hand, the machine in Station B needs periodic reset-up by the technician. Specifically, a reset-up is needed every time the machine has processed 10 jobs. The mean reset-up time is 1 hour, and the coefficient of variation of the reset-up time is 1.

The jobs are arriving at the upstream station at the rate of 1.2 jobs per hour, with a coefficient of variation of the inter-arrival time being 1.3.

(a) (20 marks) Compute the following quantities for each station:

(i) its effective process time

(ii) its coefficient of variation of process time.

(b) (25 marks) Assume that the effective process times and the coefficients of variation of the process time you've got in part (a) are as follows:

Station A: 35 min., 1.25; Station B: 25 min., 1.10

(Note: these are not necessarily the correct answers for (a)!)

Based on these assumptions, compute the average time duration a job spends in each station.

(c) (10 marks) In an effort to increase the throughput, your manager wants to increase the rate of the jobs arriving at the upstream station. Based on the same assumption as stated in (b), what would be the maximum possible rate?

(d) (25 marks) Again, assume that the effective process time for the stations are: 35 min. for Station A, and 25 min. for Station B, but now, assume that with the new technical upgrades, the coefficients of variation of the process times become practically zero: i.e. ( ) ( ) 0 e A e B c c . (i) If the jobs are arriving at the upstream station with the inter-arrival time being exactly 50 minutes: -

How much time would a job spend in the line? -

What is the corresponding WIP of the line?

(ii) Instead, if we fix the WIP of the line to be 4 jobs: -

How much time would a job spend in such a line? -

What is the corresponding throughput of such a line?