Exercise 2 A manufacturing process always has 8 parts in process. A part must successfully complete two steps (step 1 and step 2) to be completed. A single machine performs step 1 and can process an average of 8 parts per minute. A single machine performs step 2 and can process 11 parts per minute. Unfortunately, step 2 is not totally reliable. (Step 1 is totally reliable, however.) Each time a part is sent through step 2, there is a 10% chance that step 2 must be repeated. a) Find the steady-state distribution of parts at each machine. b) Find the average number of parts at each machine. c) Find the probability that each machine is busy. d) Find the number of parts per minute successfully completing service at each machine.

Exercise 2 A manufacturing process always has 8 parts in process. A part must successfully complete two steps (step 1 and step 2) to be completed. A single machine performs step 1 and can process an average of 8 parts per minute. A single machine performs step 2 and can process 11 parts per minute. Unfortunately, step 2 is not totally reliable. (Step 1 is totally reliable, however.) Each time a part is sent through step 2, there is a 10% chance that step 2 must be repeated. a) Find the steady-state distribution of parts at each machine. b) Find the average number of parts at each machine. c) Find the probability that each machine is busy. d) Find the number of parts per minute successfully completing service at each machine.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Exercise 2

A manufacturing process always has 8 parts in process. A part must successfully

complete two steps (step 1 and step 2) to be completed. A single machine performs step

1 and can process an average of 8 parts per minute. A single machine performs step 2

and can process 11 parts per minute. Unfortunately, step 2 is not totally reliable. (Step 1

is totally reliable, however.) Each time a part is sent through step 2, there is a 10%

chance that step 2 must be repeated.

a) Find the steady-state distribution of parts at each machine.
b) Find the average number of parts at each machine.
c) Find the probability that each machine is busy.
d) Find the number of parts per minute successfully completing service at each

machine.

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Step 2: Finding the steady-state distribution of parts at each machine

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Step 3: Determine average number of parts at each machine

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Step 4: Determine probability that each machine is busy

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Step 5: Determine Number of parts per minute

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