A production process contains a machine that deteriorates rapidly in both quality and outputunder 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 ConditionGood as newOperable-minimum deteriorationOperable-major deteriorationInoperable23The process can be modeled as a Markov Chain with its (one-step) transition matrix P given by171-16 8 16311P =8.48.112a. 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 iseither "Operable-major deterioration" or "Inoperable".c. According to the replacement rule in b., what is the percentage ofmachines that are replaced when they are inoperable?

a. State 0 - Machine is good as new State 1 - Machine is operable minimum deterioration State 2-…

Answered: Determine the expected life of a new…

Determine the expected life of a new machine if it is replaced when it is either "Operable-major deterioration" or "Inoperable".

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter10: Introduction To Simulation Modeling

Section: Chapter Questions

Problem 41P: At the beginning of each week, a machine is in one of four conditions: 1 = excellent; 2 = good; 3 =...

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Concept explainers

Forecasting

Forecasting is a methodology that uses historical data as inputs to make well-informed predictions about the course of future trends. Forecasting is the method of making forecasts based on historical and current data, most commonly by trend analysis. In the business world, forecasting is a basic statistical task. Forecasting is used by businesses to decide how to allocate their budgets or prepare for expected expenditures in the future. Forecasts help managers formulate and execute production plans by providing forecasts. The primary goal of forecasting is to make accurate predictions.

Question

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
2
3
The process can be modeled as a Markov Chain with its (one-step) transition matrix P given by
1
7
1
-
16 8 16
3
1
1
P =
8.
4
8.
1
1
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?

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