solution

A small factory consists of a machine and an inspector, as shown in Figure 1. Unfinished parts arrive to the factory with exponential interarrival times having a mean of 1 minute. Processing times at the machine are uniformly distributed on the interval (0.65. 0.70) minute, and subsequent inspection times at the inspector are uniformly distributed on the interval (0.75, 0.80). (The assumption of uniformity is for ease of exposition, and is not likely to be valid in a real-world application). Ninety percent of inspected parts are “good” and leave the system immediately; 10 percent of the parts are “bad” and are sent back to the machine for rework. (Both queues are assumed to be infinite capacity). The machine is subject to randomly occurring breakdowns. In particular, a new (or freshly repaired) machine will break down after an exponential amount of calendar time with a mean of 6 hours. Repair times are uniform on the interval [8, 12] minutes. If a part is being processed when the machine breaks down, then the machine continues where it left off upon the completion of repair. Assume that the factory is initially empty and idle.

0.9 Good Machine Tapeter . Bad

The factory gets an order to produce 2000 parts and thus, a simulation of this system can be considered to be terminating with E = {2000 parts have been completed). Let T be the time required to complete the required 2000 parts.