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ReliaSoft > Software > RENO > Examples > Example G-2

RENO: Probabilistic Event and Risk Analysis Visual Stochastic Event SimulatorSM
Flowchart and solve the most complex probabilistic problems.

EXAMPLES


Example G-2 - Markov Type Problem

Software Used: 
RENO


Problem Statement:

This example presents multiple solution approaches to the following simple problem:

Assume you have a community of 100 people.

  • Initially, 83 of the people are healthy and 17 are sick.
  • You predict that each year 20% of the healthy people will get sick.
  • Furthermore, 25% of the sick people will die and the remainder will get better.

You want to know how many people will still be alive after 1, 2 ... 30, years.

RENO Solution:

Define three Storage Variables to represent the number of people who are healthy, the number sick and the number dead. Note that the initial value for Healthy is 83 and the initial value for Sick is 17.

Define a fourth Storage Variable to represent the new number of people who are sick each year.

NewSick Storage Variable

There are several possible ways to construct the Flowchart. For instance:

Flowchart to model the problem

Step 1: Use a Standard Block to calculate the number of people who died during the year, which is equal to 25% of the number sick, and add that figure to the number already dead. Store this value in the Storage Variable "Dead," replacing the previous year's figure, and pass it to the next block.

Standard Block to calculate number who died during year

Step 2: Use a Result Storage of type Array to hold the number dead for each year.

Result Storage (Array)

Step 3: Use a Standard Block to calculate the number of people who became sick during the year and store this value in the Storage Variable "NewSick."

Standard Block to calculate number who fell sick during the year

Step 4: Use a Standard Block to determine the number of people who were healthy at the end of the year. This is calculated by subtracting the number of people who became sick during the current year from the number of healthy people from the previous year, then adding the 75% of the previous year's sick year who recovered. Store this value in the Storage Variable "Healthy," replacing the previous year's figure.

Standard Block to calculate number healthy during year

Step 5: Use a Standard Block to place the value of NewSick (the number of people who became sick during the current year) into the Storage Variable "Sick," replacing the previous year's figure.

Standard Block placing value of NewSick into Sick for the year

Step 6: Create a loop to repeat this process through year 30, using a Goto Flag, a Flag Marker, a Counter Block that keeps track of how many loops have been performed and a Conditional Block that tests whether the number of loops is less than or equal to 30. If it is, the Conditional Block passes a 0 down the TRUE path, continuing the simulation. If the number of loops is greater than 30, the Conditional Block passes a 0 down the FALSE path to a Stop Flag, halting the simulation.

Conditional to determine number of loops

Because all probabilities are fixed, you will need to run only one simulation. When simulation is complete, click the Show Simulation Details button [...] to view the results of the Result Storage Block "Dead." The cumulative number of people dead at the end of each year is displayed. Note that in the figure shown next, only the first ten years are shown.

Simulation Results Explorer

The plot of these results looks like the one shown next.

Result Storage Plot

A RENO project with the solution for this example (called "Markov Type Problem.rnp") is shipped with the software and stored in the Examples\General folder in the application directory (e.g. C:\Program Files\ReliaSoft\RENO\Examples\General\Markov Type Problem.rnp).

 

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October 2008
October 15 - 17, 2008: RS 525 Probabilistic Event Analysis in Tucson, Arizona
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