When a part arrives to a manufacturing system, it is first drilled by a single drill press. It is then washed by a single washer. After that, it is tested by a single inspector. If it passes the test, it leaves the system. On the other hand, if it fails the test, it is sent back (to the end of the washer queue if the washer is busy) and re-washed, instead of leaving; such a re-washed part must then undergo the same inspection, and has the same probability of failing. Every facility (drill press, washer and inspector) has its own First-In-First-Out queue with unlimited queue length for parts. (a) Define the system state at time t as [D(t), W(t), I(t)], where D(t) = the number of parts in the drilling center and its queue W(t) = the number of parts in the washing center and its queue I(t) = the number of parts in the inspection center and its queue Let [d, w, i] be the current state of the system. Define events and write the corresponding state transitions. (b) Now, suppose that the washer is subject to failures. It is assumed that the washer fails ONLY while washing a part, and that on repair completion, the suspended washing process continues from the point of interruption. Define the system state at time t as [D(t), W(t), S(t), I(t)], where D(t) = the number of parts in the drilling center and its queue W(t) = the number of parts in the washing center and its queue S(t) = the status of the washer (0=idle, 1=busy, 2=down) I(t) = the number of parts in the inspection center and its queue Let [d, w, s, i] be the current state of the system. Define events and write the corresponding state transitions