Main-Effect Plans Orthogonal Through the Block Factor

Abstract

Many industrial experiments require different number of levels for different factors. Orthogonal main-effect plans (OMEPs) for such asymmetrical experiments often require large run size. If blocking is needed, then run size usually becomes even larger. In this article we show that there are situations when use of blocks may in fact be helpful in finding an OMEP with small run size. Explicitly, we obtained saturated OMEPs for a 33n⋅23n experiment in 3n blocks of size 4 each for each Hadamard number n. In each of these plans, the three-level factors are nonorthogonal to the block factor but are pairwise orthogonal through the block factor. The two-level factors are orthogonal to the block factor. The data analysis for such a plan is illustrated with the help of examples. This article has supplementary material online.