In a production line suppose that there are k stations in series (see Figure) - Assume that jobs arrive at station 1 from an infinite source according to a Poison process with mean rate ( per unit time. The output from station 1 is used as input to station i + 1. Because there are defective items at each station, the percentage of good items from station i is equal to 1000αi, 0 ( αi, ( 1. The remaining percentage 100(1 - αi) represents the defective: at station i. Assume that service time at station i is exponential with mean rate (i per unit time.
(a) Derive a general expression for determining storage space associated with each station i such that all arriving (good) items can be accommodated 8% of the time.
(b) Let ( = 20 items per hour and (i = 30 items per hour for all stations. Percentage of defective items at each station may be assumed constant and equal to 10%. Give a numerical answer for part (i) given k = and, β = 95%.
(c) Using the data in part (ii), what is the expected number of defective items from all stations during a period of T hours? What is your answer when T = 8 hrs?