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A production process contains a machine that deteriorates rapidly in both quality and output under heavy usage, so that it is inspected at the end of each day. Immediately after inspection, the condition of the machine is noted and classified into one of the four possible states: Condition Good as new State Operable-minimum deterioration Operable-major deterioration Inoperable 1 2 3 The process can be modeled as a Markov Chain with its (one-step) transition matrix P given by

A production process contains a machine that deteriorates rapidly in both quality and output under heavy usage, so that it is inspected at the end of each day. Immediately after inspection, the condition of the machine is noted and classified into one of the four possible states: Condition Good as new State Operable-minimum deterioration Operable-major deterioration Inoperable 1 2 3 The process can be modeled as a Markov Chain with its (one-step) transition matrix P given by

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 12EQ: 12. Robots have been programmed to traverse the maze shown in Figure 3.28 and at each junction...
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A production process contains a machine that deteriorates rapidly in both quality and output under heavy usage, so that it is inspected at the end of each day. Immediately after inspection, the condition of the machine is noted and classified into one of the four possible states: State Condition Good as new Operable-minimum deterioration Operable-major deterioration Inoperable 1 2 The process can be modeled as a Markov Chain with its (one-step) transition matrix P given by 1 7 16 8. 3 P = 4 2 a) Determine the expected life of a new machine if it is replaced when it is "Inoperable". b) Determine the expected life of a new machine if it is replaced when it is either "Operable-major deterioration" or "Inoperable". c) According to the replacement rule in b., what is the percentage of machines that are replaced when they are inoperable? 1/01INI -으-18l_20
Transcribed Image Text:A production process contains a machine that deteriorates rapidly in both quality and output under heavy usage, so that it is inspected at the end of each day. Immediately after inspection, the condition of the machine is noted and classified into one of the four possible states: State Condition Good as new Operable-minimum deterioration Operable-major deterioration Inoperable 1 2 The process can be modeled as a Markov Chain with its (one-step) transition matrix P given by 1 7 16 8. 3 P = 4 2 a) Determine the expected life of a new machine if it is replaced when it is "Inoperable". b) Determine the expected life of a new machine if it is replaced when it is either "Operable-major deterioration" or "Inoperable". c) According to the replacement rule in b., what is the percentage of machines that are replaced when they are inoperable? 1/01INI -으-18l_20
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