When optimizing a complex system by determining the optimum condition of the system parameters of interest, we often employ the process of estimating the unknown objective function, which is assumed to be a second order spline function. In doing so, we normally use common random numbers for different set of the controllable factors resulting in more accurate parameter estimation for the objective function. In this paper, we will show some mathematical result for the analysis of variance when using common random numbers in terms of the regression error, the residual error and the pure error terms. In fact, if we can realize the spe structure of the covariance matrix of the error terms, we can use the result of analysis of variance for the uncorrelated experiments only by applying minor changes.
I. Introduction
II. Correlated Simulation Experiments
III. The ANOVA Table for Special Covariance Structure using Common Random Numbers
IV. Conclusion and Further Research Topic
Appendix
References