07-01-2014, 03:15 PM
Markov Analysis
Markov Analysis.ppt (Size: 717.5 KB / Downloads: 216)
Introduction
This discussion will be limited to Markov problems that follow four assumptions
There are a limited or finite number of possible states
The probability of changing states remains the same over time
We can predict any future state from the previous state and the matrix of transition probabilities
The size and makeup of the system do not change during the analysis
States and State Probabilities
States are used to identify all possible conditions of a process or system
It is possible to identify specific states for many processes or systems
In Markov analysis we assume that the states are both collectively exhaustive and mutually exclusive
After the states have been identified, the next step is to determine the probability that the system is in this state
The Vector of State Probabilities for Three Grocery Stores Example
States for people in a small town with three grocery stores
A total of 100,000 people shop at the three groceries during any given month
Forty thousand may be shopping at American Food Store – state 1
Thirty thousand may be shopping at Food Mart – state 2
Thirty thousand may be shopping at Atlas Foods – state 3
Predicting Future Market Shares
One of the purposes of Markov analysis is to predict the future
Given the vector of state probabilities and the matrix of transitional probabilities, it is not very difficult to determine the state probabilities at a future date
This type of analysis allows the computation of the probability that a person will be at one of the grocery stores in the future.
Since this probability is equal to market share, it is possible to determine the future market shares of the grocery stores
Markov Analysis of
Machine Operations
The owner of Tolsky Works has recorded the operation of his milling machine for several years
Over the past two years, 80% of the time the milling machine functioned correctly for the current month if it had functioned correctly during the preceding month
90% of the time the machine remained incorrectly adjusted if it had been incorrectly adjusted in the preceding month
10% of the time the machine corrected to problems and operated correctly when it had been operating incorrectly