Section F (Questions 19 ~ 24): A production line consists of…
Section F (Questions 19 ~ 24): A production line consists of two stations: one for production (Station A) and one for checking (Station B). Station A has job arrivals from outside, following a Poisson arrival process with rate 11/hr (a1 = 11/hr) and internal job arrivals from station B. A study shows that 50% of jobs produced at station A do not require checking but the other 50% of jobs are sent to the checking station (Station B). Station B gets an outside arrivals following a Poisson process with rate 5/hr (a2 = 5/hr). Among jobs at station B (both jobs from the outside and from station A), only 40% do not have defectives and leave the system. But the remaining 60% jobs need to be processed again at Station A and sent back to the end of the wait line of Station A. A defective item can visit stations A and B several times until it is fully fixed. A diagram of the production line is given below: Station A has three servers and each processes one job at a time with a normally distributed service time with mean 6 minutes and variance 2 minutes2. Station B has one server and its processing time is also normal with mean 3 minutes and variance 0.25 minutes2.