Calculation of probability distributions of output variables in process simulation

Stochastic process analysis is often based on Monte Carlo simulations. As a more rigorous alternative, a deterministic algorithm based on numerical integration is proposed in this paper, which calculates the probability distributions of dependent random variables using the results of simulation at grid points of independent random variables. For performance evaluation, the proposed algorithm is applied to an example problem which can be analytically solved, and the result is compared with that of Monte Carlo simulation. The proposed algorithm is suitable for general process simulation problems with a few independent random variables, and expected to be applicable to areas such as safety analysis and quality control.