1.4 Simulation
Many real world systems are stochastic. A tool to study such systems is simulation, i.e., a model of the system is built which makes it possible to simulate the behavior of the system. By collecting data during the simulation information on important properties of the system can be gained. An example of such a system and what can be gained by simulation is given below.A certain machine uses a type of part which is subject to periodic failure. Whenever the in-use part fails, the machine must be turned off. The failed part is then removed, a good spare part is installed if available, or as soon as one becomes available, and the machine is turned on again.
The lifetime of a part is normally distributed, with the mean 350 hours and the standard deviation 70 hours. It takes 4 hours to remove a failed part from the machine. The time required to install a replacement part is 6 hours. Repair-time for a failed part is normally distributed, with mean and standard deviation of 8 and 0.5 hours, respectively.
The machine operator himself is responsible for removing the part from the machine, and installing a replacement in its place. There is a repairman who is responsible for repairing failed parts. The repairman's duties also include repair of items routed to him from another source. These other items arrive according to the negative exponential distribution with a mean interarrival time of 9 hours. Their service-time requirement is 8 ± 4 hours. These other items have higher repair priority than the failed parts used in the machine of interest, however, an ongoing repair activity is not interrupted.
How does the number of stored spareparts influence on the up-time of the machine?
Data to collect during simulation for the system above is the up-time and the simulation must be performed for spareparts equal 0,1,2,... .
We will learn how such systems can be modeled and how the models can be implemented to make simulations possible.