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Consider a flexible manufacturing system in which 10 parts are always in process. Each part requires two operations. Each part begins by having operation 1 done at machine 1. Then, with probability .75 the part has operation 2 processed on machine 2, and with probability .25 the part operation 2 processed on machine 3. Once a part completes operation 2, the part leaves the system and its immediately replaced by another part. Consider server rates exponentially. ₁.25 minutes H₂ = .48 minutes 3.08 minutes a. Find the probability distribution of the number of parts at each machine. b. Find the expected number of parts present at each machine c. What fraction of time is each machine busy? d. How many parts per minute are completed by each machine?

Consider a flexible manufacturing system in which 10 parts are always in process. Each part requires two operations. Each part begins by having operation 1 done at machine 1. Then, with probability .75 the part has operation 2 processed on machine 2, and with probability .25 the part operation 2 processed on machine 3. Once a part completes operation 2, the part leaves the system and its immediately replaced by another part. Consider server rates exponentially. ₁.25 minutes H₂ = .48 minutes 3.08 minutes a. Find the probability distribution of the number of parts at each machine. b. Find the expected number of parts present at each machine c. What fraction of time is each machine busy? d. How many parts per minute are completed by each machine?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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* Consider a flexible manufacturing system in which 10 parts are always in process. Each part requires two operations. Each part begins by having operation 1 done at machine 1. Then, with probability .75 the part has operation 2 processed on machine 2, and with probability .25 the part operation 2 processed on machine 3. Once a part completes operation 2, the part leaves the system and its immediately replaced by another part. Consider server rates exponentially. H=.25 minutes H2= 48 minutes H3 =.08 minutes a. Find the probability distribution of the number of parts at each machine. b. Find the expected number of parts present at each machine C. What fraction of time is each machine busy? d. How many parts per minute are completed by each machine?
Transcribed Image Text:* Consider a flexible manufacturing system in which 10 parts are always in process. Each part requires two operations. Each part begins by having operation 1 done at machine 1. Then, with probability .75 the part has operation 2 processed on machine 2, and with probability .25 the part operation 2 processed on machine 3. Once a part completes operation 2, the part leaves the system and its immediately replaced by another part. Consider server rates exponentially. H=.25 minutes H2= 48 minutes H3 =.08 minutes a. Find the probability distribution of the number of parts at each machine. b. Find the expected number of parts present at each machine C. What fraction of time is each machine busy? d. How many parts per minute are completed by each machine?
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