1. Modeling and Analysis of Manufacturing Systems: Flow Lines Kimberly Murdoch MEAE6960 - MAMS Prof. E. Gutierrez-Miravete April 19, 2001

2. Analysis Assumptions Mean Cycles to Failure is a continuous geometric RV equal to 1/  cycles;  =failure rate Repair time is a geometric RV with an average of 1/b cycles. Uptime and Downtime RV’s are independent Idle stations do not fail Failures only occur at the end of a cycle Failure of only one station is allowed per cycle The first station in the system is never starved The last station in the system is never blocked Transfer through the buffers takes zero time

3. Paced Line without Buffer WS 20WS 3  WS 2WS 1   20 Workstations Cycle Time, C=10 seconds Repair rate, b=1/30  1 =  2 = 

4. Paced Line without Buffer

5. Paced Line with Buffer Buffer Z WS 20WS r  WS 2WS 1   Buffer Z 2’2’ 1’1’ WS “2”WS “1” Reduces to... 20 Workstations Cycle Time, C=10 seconds Repair rate, b=1/30  1 =  2 =  =0.0005 Buffer size = Z

6. Paced Line with Buffer               1, )1()]1(1)[21( )1()1(1 1, )1(1 1 2 22 22 21 s xZbxbrx x xbr s sCxx E Z Z Z 1 2 x x s  1 2    r i i i b x   )())(( )() ( 2121122121 2121212121 bbbbb bbbbb C     