Optimal assignment of samples to treatments for robust design

Abstract

A series of experiments was performed to test the appearance of wood samples after treatment and accelerated weathering. In the initial experiments, treatment effects were obscured by the high variability between the wood samples. The wood samples can be characterized, but their properties cannot be changed or controlled. Subsequent experiments were designed using robust and optimal design techniques. The characteristics of the wood samples were measured and included as noise variables. The wood samples were selected and assigned to treatments using the D-optimal criterion. Control-by-noise interaction effects were included in the presumed model where possible. The resulting designs yielded significant treatment effects. Approximately half of the variability in the appearance after weathering can be attributed to the characteristics of the wood samples. After removing the variability due to the wood itself, most of the remaining variability in the appearance of the wood can be attributed to the treatments.