Broke & Down has several hundred machines in its large manufacturing facility as it uses the

PWP concept (plant-within-a-plant).

Ray Pear, Manager of Maintenance and Chief Mechanic for

the Broke & Down Machine Shop, says that broken machines arrive at the repair facility

according to a Poisson pattern at the average rate of 2 per 8-hour day.

Ray likes to remind his

boss, Mr. I. M. Broke, that since he is such a master mechanic he is the only person needed to

repair the broken machines, and he can repair a machine in just 2 hours on average.

Furthermore, the repair time follows an exponential distribution, and Ray repairs the machines in

the order in which they break down.

Assuming that the machine shop operates 8 hours per day:

(a)

if a machine breaks down, what is the probability that Ray can begin work on it

immediately?

(b) on average, how long is a broken machine out of service?

(c)

on average, how many machines are awaiting repair?

(d) Mr. Churchill Down, co-owner of the machine shop is concerned that too much productive

time is being lost due to machine break downs.

He agrees that Ray is a super mechanic but

also thinks that Ray needs help so the shop would have less downtime waiting for repairs.

Churchill knows of Ray's son Desmond, often called Des for short.

Des is also a master

mechanic and Churchill has been considering hiring Desmond for some time if it is

economically feasible.

Master mechanics are paid $20 per hour, and the machines produce

revenue at $60 per hour when in service.

Should Des Pear be hired?

(e)

I. M. Broke is not too keen on the idea of hiring Des Pear as it has a flavor of nepotism.

I. M.

suggests that to help Ray they could invest in more sophisticated diagnostic equipment and

repair tools that would reduce Ray's average repair time to 1 hour and 20 minutes (i.e. 4/3

hours).

If these more sophisticated tools and equipment cost Broke & Down $20 per hour to

operate, and Ray is paid $20 per hour, should the investment be made?

Again, the machines

produce revenue at the rate of $60 per hour when in service.

(f)

Anna Last, Director of Corporate Analytics for Broke & Down suggests that the use of the

more sophisticated equipment (part e) not only shortens the average repair time but also the

associated variability and changes the distribution of the repair time so it is no longer

exponential.

From discussions with the manufacturer of the equipment, it is estimated that

the standard deviation of the repair time is 1 hour.

Does this change what I.M. should do?

Show/explain