An application of information theory and error-correcting codes to fractional factorial experiments

The objective of design of experiments (DOE) is addressed by introducing an information optimality criterion, which is based on concepts adopted from information theory. In particular, experiments are specified to maximize the information in the system responses about estimators of the system parameters. It is shown that one has to maintain certain resolution of the design matrix to maximize the information, obtainable by a design, about a system described by a linear model with interactions. The correspondence between error-correcting codes and fractional factorial experiments provides a method to attain the required resolution with a smaller fractional factorial experiment by increasing the number of levels associated with each factor - a result that in the context of experimental design seems counterintuitive. In particular, the Gilbert-Varshamov and the Singleton bounds are employed to obtain bounds on the size of the fractional experiment. Analytical approximations and numerical results are given and illustrated by examples.