Second-order extensions to nearly orthogonal-and-balanced (NOAB) mixed-factor experimental designs

ABSTRACT

When simulation studies involve many quantitative (i.e., discrete and continuous) and qualitative (i.e., categorical) input factors with different numbers of levels for each, meta-models of simulation responses can benefit from the use of mixed-factor space-filling designs. The first-order nearly orthogonal-and-balanced (NOAB) design is a popular approach in these situations. This research develops second-order extensions for an existing construction method of NOAB designs, estimating the pairwise correlations between possible first-order and second-order terms. These extensions permit additional linear constraints in the mixed-integer linear programming (MILP) formulations previously developed for first-order NOAB designs. A case study is presented for NOAB designs of different sizes and construction approaches. The second-order MILP extensions show improvements in design performance measures for parameter estimation and prediction variance for an assumed second-order model as well as for model misspecification with respect to second-order terms for an assumed first-order model.

KEYWORDS:

• Design of experiments
• mixed-integer linear programming
• pairwise correlation
• model misspecification
• meta-model

Acknowledgement

This research is in support of the Simulation and Analysis Facility (SIMAF), Air Force Life Cycle Management Center, Simulation and Analysis Division (AFLCMC/XZS). The views expressed in this article are those of the authors and do not reflect the official policy or position of the United States Air Force, Department of Defense, or the U.S. Government.

Disclosure statement

No potential conflict of interest was reported by the authors.