Analytic approach & Monte Carlo methods for realistic systems analysis Original Research Article

The basic concepts of system Engineering are briefly described. The general problem is outlined as that of a `particleʹ moving in a phase space of states and time. It is shown that this general view leads to a transport equation underlying the behavior of systems. The transport equation is presented with some details and a number of special cases of the equation are discussed in details. The Monte Carlo method is then presented as a general and exclusive means for the solution of this transport equation. While this discussion is highly theoretical an effort is made to maintain the overall perspective that the final purpose is to obtain solutions for realistic industrial problems. A set of unbiased estimators are then presented and proved. Basic methods for variance reduction using transformations of the absorption probability are presented and discussed.