TABLE OF CONTENTS There are many situations in probabilistic risk analysis when there is no analytic algorithm that will evaluate the required probabilities. Alternatively, the available algorithm is extremely complex and can only be carried out at great expense of effort and computer time.
An alternative method is known as Monte Carlo simulation. It depends on the fact that the histogram of a large random sample approximates the probability function of the underlying random variable.
Suppose that the output variable required to carry out the risk analysis, denoted by Y, is given as a function of a vector X of underlying variables: X= ( X 1, , X n) in the form
In the Monte Carlo method, a random sample of size N of the vector of underlying variables X 1, , X N is generated. Each such vector is called a realization of the vector X. To each realization there corresponds a value of the output variable Y. Thus we obtain a sample of size N from the output variable Y. Provided N is chosen appropriately large, the histogram of Y will approximate its distribution as closely as required.
Example As an example, we shall consider a floor of a building consisting of four compartments numbered 1 to 4 and we want to study fire spread from compartment 1 to compartment 4.
For the purpose of investigating fire spread from one...
