A study on the construction of the orthogonal block designs in mixture experiments

In varieties of industrial research including film, food, petroleum, pharmaceuticals, and rubber, the product is a mixture of several ingredients. An important problem is to find the optimum proportions of ingredients in order to maximize the product performance. Mixture experiments include effective tools in determining such optimum proportions. So, mixture experiments play an important role in quality improvements studies of the companies. In this study, the designs that are used in experiments with mixtures are examined. Scheffé models are mentioned and then the alternative models of Scheffé models are introduced. After that, general method of constructing designs for q 3 mixture components in two or more orthogonal blocks are examined. The designs are built from Latin squares with specific properties and are generalizations of those for four and five components given by Draper and Prescott.