A manufacturer of engine belts uses multipurpose manufacturing equipment to produce a variety of products. A technician is employed to perform the setup operations needed to change the machines over from one product to the next. The amount of time required to set up the machines is a random variable that follows an exponential distribution with a mean of 20 minutes. The number of machines requiring a new setup is a Poisson random variable with an average of two machines per hour requiring setup. The technician is responsible for setups on five machines.
a. What percentage of time is the technician idle, or not involved in setting up a machine?
b. What should the technician do during this idle time?
c. On average, how long is a machine out of operation while waiting for the next setup to be completed?
d. If the company hires another equally capable technician to perform setups on these machines, how long on average would a machine be out of operation while waiting for the next setup to be completed?