Each item is inspected and is declared to either pass or fail. The machine can work in automatic or manual mode. If it outputs two failed items in a row in automatic mode, it is switched to manual. Once it produces two passing items in a row in manual mode, it is switched back to automatic. Sup- pose that failure rate is a in automatic and b in manual. You modeled the system as a Markov chain with a diagram given below, where states represent the mode and the status of the previously man- ufactured item, so for example, state “manual-1 success” represents that the machine is in manual mode and the previous item passed. automaticno failuretaautomaticIfailuvemanualno successmanualI success1-6i. Suppose that a = 0.17 and b = 0.03. Write down the system of equations to determine thelong-run state proportions.ii. Suppose that the solution is 0.813 for state "automatic-no failure" and 0.025 for state "manual-no success". Determine the rest of the long run proportions.iii. Find the proportion of items produced in the manual mode.iv. Find the proportion of items that fail the inspectionv. Suppose that manufacture time is 2 minutes in the automatic mode and 11 minutes in the manualmode. How many items can be produced in an 8 hour shift?

Ans-i. The system of equations to determine the long-run state proportions is given by: 0.17x +…

Answered: Each item is inspected and is declared…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Each item is inspected and is declared to either pass or fail. The machine can work in automatic or manual mode. If it outputs two failed items in a row in automatic mode, it is switched to manual. Once it produces two passing items in a row in manual mode, it is switched back to automatic. Sup- pose that failure rate is a in automatic and b in manual. You modeled the system as a Markov chain with a diagram given below, where states represent the mode and the status of the previously man- ufactured item, so for example, state “manual-1 success” represents that the machine is in manual mode and the previous item passed.