Test 1 White Sol 2010

Test 1 White Sol 2010 - ISEN 316 TEST 1 2—26 WHITE...

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Unformatted text preview: ISEN 316 TEST 1 2—26 WHITE Instructions: Use the front of your solutions papers only. Place the exam on top of your answers and staple them together in the left top corner. Write your name and UIN on the top of this sheet. 36 points I I. Consider an experiment where two die (a pair of dice) (red and blue) are tossed simultaneously. Both dies are 6 sided with equal areas (equal probabilities of each side ending up on the top). The red die, however, is unusual in that it has two sides With 1’s and two sides with 2’s, one side with a 3 and one side with a 4 (these are numbers or dots, whichever you want to consider). (a) What is a sample space for this experiment (define it, since there is more than one way of doing this!) List all the outcomes. (b) How many events are there for this experiment. (c) What is the event that the sum of the top faces equals 4. That is, what are the outcomes that make up this event? (cl) What is the probability of the event of (c) occurring? 36 points . 2. Consider a E2 / M I 2/ 4 system, with a mean arrival rate of it and a mean service rate per machine of p . (a) Define a state-space to represent this system probabilistically. (b) Draw the rate—based state-diagram of the system (connecting the system states). - - (c) Develop the steady—state equation relating the state probabilities by isolating on the state where the system is fill] and the arrival process is in the second phase. (d) Write the equation (using the state probabilities) for the WIP in the system. 28 points 3. Consider two workstation serial factory as depicted by the diagram below: - Compute the factory cycle time, throughput and work-in—process. Assume the following data is known: ' ' 21 =Sjobs/hr C§(1)=2 E[S,] =1/7 hrs C2[Sl]= 1.5 E[Sz]=10 min C2[Sz] =3 10 points bonus 4. Define the following terms: (a) Little’s Law (b) Utilization (c) Steady-state probabilities .Sxambxesplace *3" (11¢ on Red qfe I 1% on blue Ed‘fe‘g , {C M09031), (1.3), mm, H.933, (Mex (233, (1(2)) (2133, C2,H7,<2,5‘>, (2,67,/ (3,0, (3,2), (33"), (3m, (3,5),(3gm mm, (m, (4,3); Mm, (mm (mg/g @ E.1)M/2/L! svsw-em A. M 1:114 “W WA Em CED (armamhase; fl) 7 K: \OR2 L.) n:- 4¢ gaps ‘m svs+em n: 0,1,23H / (MWZP. " J I J (27%y'p2g coo I ICWe—Hme 2?: +hROUQh§3W€E WORk‘m“PROC€SS: 3 N:- 5 calm? EESA= V7 Czisflflb £92]: V6 M92313 * I woRkS‘ra'f‘f’O’D 1: __ v '2’ ’2, _, . CTS—(Ca +CS) t[sj+E[S] 7. Ca“(n=2 =C1ESJ:\°5 U: AEESJT-SW/Tfish ..'t ‘ 63:34?“ 1/5 5// L” / ' 5 I 7: a 7 ‘I+\ w ( ,2 )(Wh/T /—, cTsmz (19763005.) (m +l/7 chm: 05167857 = L43/593. WkPm': )\CTS ;5(q3/56)_ :- 3.3301 2 “5/56 GEM]: C121 :2 (HF) 63+ LEG-[sf] _ 01d -‘- 045/717") (“13+ (5/751057 624 = 09m 50: :2- 0.1653 C3: LT—Hq / - + - MS EfSfl=’/s vim-:3 C§=Czofm=L7LIl~lcf CTS: (caHCsZ) His] + Eli's] ‘2 Us: Mm]: 5(t/e‘)= 5/6 ./ t/ / ‘a/ CT (2): I:qu +3 5/6 1 \/ S ( '2_ >(i’3/CD /G+ G 7 . CTsm‘): Maggy/“Vs CTSCZW': 2.1% ~ W IP (23‘: A 073(2) 3/ =5(2M‘)= 20.72 *%g W‘Psvw WW3er WHM’) ‘5 3w83Cf‘1'iOJ2 = H.559 Cycle+fme= m -_- M550: .. 75.7% A 5- , +hr20ughpu+ = 5 WORKan-pflocess : H9559 @ LT++ke‘s Law: WoQk— Twmocess = Gt—hs‘zoughpufl MCVQWTWQ ' / @ ufilfzafioni U: AEETS‘E :— A“ c MC r W 5 how much 0+ +he Svs+em as Sci-wally bemg U860} 15. ,p , / 7/ fl . © smadw s+a+e mom WHFESE GTven +he 8V8+6m ?S m s+eaqws+a+e +he PRObapTIHTes of each dfFFejggm+ sJyaJce occumhge Fora exampxe B =' W8 DT-‘zobabflfw when meme 3-1263 fiQfObS Th +he 3VS+€m EPnr-l gall- +he : PROPOSIDWHBS mu3+ ado! upwrl 7 UMJw 69‘ w 0% / ‘i/o ...
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Test 1 White Sol 2010 - ISEN 316 TEST 1 2—26 WHITE...

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