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

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

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

Paced Line without Buffer

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

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