### Experiment Design in Non-Traditional Settings

Organizers: Joe Voelkel, RIT and Ron Kenett, KPA Management ConsultingSession Chair: Joe Voelkel, Rochester Institute of Technology

**The Use of Common Random Numbers with Stochastic Kriging**

Bruce Ankenman

Northwestern University

Stochastic Kriging is a recently introduced method for creating response surface models for discrete event simulation output. I will briefly introduce discrete event simulation and motivate the use of both Stochastic Kriging and Common Random Numbers (CRN), which is a blocking-like technique. I will then present both analytic and empirical results for how the use of CRN affects the fitting of the Stochastic Kriging response surface. I will show that if the primary purpose of the response surface is optimization or parameter estimation, then use of CRN is beneficial, however, if the primary purpose is prediction, then CRN is detrimental.

**Recent Advances on Computer Experiments**

Dennis K.J. Lin

The Pennsylvania State University

This talk attempts to address the fundamental question of "what is a (proper) computer simulation?" Specifically, this talk will be focused on design of running computer simulation models. Computer models can describe complicated physical phenomena. However, to use these models for scientific investigation, their generally running times and mostly deterministic nature require a special designed experiments. Recent advances on Latin Hypercube Design and Uniform Design will be discussed. Furthermore, various simulation issues will be discussed, including, bootstrapping (re-sampling), Markov Chain Monte Carlo (MCMC), Statistical Distribution, random number generation, and computer models. Their basic concepts and usefulness will be discussed, no specific algorithm will be given, however. (Slides of can be downloaded at http://www.personal.psu.edu/users/j/x/jxz203/lin/Lin_pub/)

**Optimal Designs for Two-Level Factorial Experiments with Binary Response**

Abhyuday Mandal

^{1}, Jie Yang

^{2}and Dibyen Majumdar

^{2}

^{1}University of Georgia and

^{2}University of Illinois

We consider the problem of obtaining locally D-optimal designs for factorial experiments with qualitative factors at two levels each with binary response. For the 2

^{2}factorial experiment with main effects model we obtain optimal designs analytically in special cases and demonstrate how to obtain a solution in the general case using cylindrical algebraic decomposition. The optimal designs are shown to be robust to the choice of the assumed values of the prior and when there is no basis to make an informed choice of the assumed values we recommend the use of the uniform design, i.e., the design that assigns equal number of observations to each of the four points. For the general 2

^{k}case we show that the uniform design has a maximin property.