Sensitivity analysis and optimization of system dynamics models : Regression analysis and statistical design of experiments

This tutorial discusses what-if analysis and optimization of System Dynamics models. These problems are solved, using the statistical techniques of regression analysis and design of experiments (DOE). These issues are illustrated by applying the statistical techniques to a System Dynamics model for coal transportation, taken from Wolstenholme's book "System Enquiry: a System Dynamics Approach" (1990). The regression analysis uses the least squares algorithm. DOE uses classic designs, namely, fractional factorials and central composite designs. Compared with intuitive approaches, DOE is more efficient: DOE gives more accurate estimators of input effects. Moreover DOE is more effective: interactions are estimable too. The System Dynamics model is also optimized. A heuristic is derived, inspired by Response Surface Methodology (RSM) but accounting for constraints. Some remaining pertinent problems are briefly discussed, namely DOE for cases with many factors, and DOE for random System Dynamics models. Conclusions are presented for the case study, and general principles are derived. Finally 23 references are given for further study.