### Design of Experiments: Overview

Jack P. C. Kleijnen
2008 Social Science Research Network
Design Of Experiments (DOE) is needed for experiments with real-life systems, and with either deterministic or random simulation models. This contribution discusses the different types of DOE for these three domains, but focusses on random simulation. DOE may have two goals: sensitivity analysis and optimization. This contribution starts with classic DOE including 2 k−p and Central Composite Designs (CCDs). Next, it discusses factor screening through Sequential Bifurcation. Then it discusses
more » ... hen it discusses Kriging including Latin Hypercube Sampling and sequential designs. It ends with optimization through Generalized Response Surface Methodology and Kriging combined with Mathematical Programming, including Taguchian robust optimization. 479 978-1-4244-2708-6/08/\$25.00 Kleijnen factor in simulation; see Schruben and Margolin (1978) and also Kleijnen (008a). DOE for real-life experiments often uses fractional factorial designs such as 2 k−p designs: each of the k factors has only two values and of all the 2 k combinations only 2 k−p combinations are observed; e.g., a 2 7−4 design means that of all 2 7 = 128 combinations only a 2 −4 = 1/16 fraction is executed. This 2 7−4 design is acceptable if the experimenters assume that a first-order polynomial is an adequate approximation or-as we say in simulation-a valid 'metamodel'. A metamodel is an approximation of the Input/Output (I/O) function implied by the underlying simulation model. Besides first-order polynomials, classic designs may also assume a first-order ('main effects') metamodel augmented with the interactions between pairs of factors, among triplets of factors, . . . , and 'the' interaction among all the k factors (however, I am against assuming such high-order interactions, because they are hard to interpret). Moreover, classic DOE may assume a second-order polynomial. See Montgomery (2009), Myers and Montgomery (1995) , and also Kleijnen (008a). In deterministic simulation, another metamodel type is popular, namely Kriging (also called spatial correlation or Gaussian) models. Kriging is an exact interpolator; i.e., for 'old' simulation input combinations the Kriging prediction equals the observed simulation outputs-which is attractive in deterministic simulation. Because Kriging has just begun in random simulation, I will discuss this type of metamodel in more detail; see Section 4. Each type of metamodel requires a different design type, and vice versa: chicken-and-egg problem. Therefore I proposed the term DASE, Design and Analysis of Simulation Experiments, in Kleijnen (008a). Which design/metamodel is acceptable is determined by the goal of the simulation study. Different goals are considered in the methodology for the validation of metamodels presented in Kleijnen and Sargent (2000) . I focus on two goals: • Sensitivity Analysis (SA); • optimization.