lecture15 - MIT 2.852 Manufacturing Systems Analysis Lectu...

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Unformatted text preview: MIT 2.852 Manufacturing Systems Analysis Lectu re 1 5 EXPZTL and CONZTL performance Stanley B. Gershwin Spnng,2004 Copyright @2004 Stanley B. Gershwin. All rights reserved. Exponenflaland Confinuous Two-Machine hnes . Exponential processing time: exponential processing, failure, and repair time; discrete state, continuous time. . Continuous material, or fluid: deterministic processing, exponential failure and repair time; mixed state, continuous time. Copyright @2004 Stanley B. Gershwin. All rights reserved. Exponenflaland Confinuoqs Two-Machine hnes Exponential — discrete material, continuous time o [Lt-(St = the probability that Mi completes an operation in (t, t + 61:); o (pg-61: = the probability that M;- tails during an operation in (t, t + 61:); . n51: = the probability that M3- is repaired, while it is down, in (15,15 + 61:); Copyright @2004 Stanley B. Gershwin. All rights reserved. Exponenflaland Confinuous Two-Machine lines Stare Transition Graph for Exponentiaf Processing Tim, Two—Machine Line "=0 ":1 [3:2 0:3 [1:4 0:5 [1:5 "=7 ":6 M 9:10 [1:1 I 9:12 [1:13 =N— 1 =N / xJ“ x)“ xj“ key states rrmsfl‘fms tram our of I'rmsienl' gangs rim—transient our of non—I'mnsiem males bomdary O to increasing buffs-[M _... M: 0 r0 decreasing buffer m _.. unchanging but" W _.. Copyright @2004 Stanley B. Gershwin. All rights reserved. Exponenflaland Confinuous Two-Machine hnes Continuous — continuous material, continuous time . [Lg-(St = the amount of material that M:- processes, while it is up, in (15,15 + 61:); opicfit = the probability that M;- fails, while it is up, in (t,t-+-6t); o n61: = the probability that M:— is repaired, while it is down, in (t,t + 61:); Copyright @2004 Stanley B. Gershwin. All rights reserved. Exponenflaland Confinuous Two-Machine hnes 0T1 = 039,131 = 0.01, [1,1 = 1.1 0 r2 = 0.08.131 = 0.009 0 N = 20 0 Explain the shapes of the graphs. Copyright @2004 Stanley B. Gershwin. All rights reserved. Exponential and Continuous Two—Machine Li nee 1 0.5 0.5 0.4 0.2 Continuous — Exponentlal Exponenflaland Confinuoqs Two-Machine hnes o Explain the shapes of the 15: _ graphs. _ _ fi 3 ElIJ I 1' I H2 2 Copyright @2004 Stanley B. Gershwin. All rights reserved. 7 Exponenflaland Confinuous Two-Machlne hnes 1_ ' ' ' ' ' ' ' ' ' I _ I I I I I I I I I I I I I I I I P _ _ — Exponential - _ _ — Continuous — _ _ — filo-variability |imi1_ 0.8 — — _ 0.6 l __ : g_4 __ __ _ 0.2 l . .. . .i — — No—IIIIaI-Iablll’qf IIrnIt— _ ‘ Continuous ‘ — ‘ Exponentlal : _ D | | | | | | | | | I | | | | | | | | | I | | | | | | | D 1 2 2 l"L2 H2 Copyright @2004 Stanley B. Gershwin. All rights reserved. ...
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