Mixture Designs for Four Components in Orthogonal Blocks

Abstract

The problem of partitioning the blends (runs) of four mixture components into two orthogonal blocks when a quadratic model is fitted is considered. This is motivated by an industrial investigation of bread-making flours carried out at Spillers Milling Limited, a member of the Dalgety group of companies in the United Kingdom. The design solution proposed by John and described by Cornell is discussed and extended. Study of the characteristics of Latin squares of side 4 leads to reliable rules for quickly obtaining designs of specified kinds. One such design was selected for the experiment at Spillers Milling. Mixture-component values that cause singularity in the new designs are identified, and values that provide designs with highest D-criterion values are obtained for the class of designs discussed. Conveniently rounded, near-optimal mixture component values were chosen for the Spillers Milling experiment, and the analysis led to the prediction of an optimal flour mixture.

KEY WORDS:

• D criterion
• Latin squares
• Second-order models