Abstract: Fractional factorial designs of mixed levels two and four are often carried out in industrial experiments. A convenient method to set up such designs is to use orthogonal arrays. By applying the technique of replacement to two-level orthogonal arrays, mixed-level orthogonal arrays can be established for practical applications. Treatment combinations for the experiment can be obtained by assigning factors to appropriate columns. However, when level changes in subsequent experimental runs and trend resistance of certain effects are considered, caution must be taken on replacement in order to minimize the cost of level changes and to achieve trend resistance. In this paper, level changes and the degree of trend resistance in the resulting column from the replacement are explored. When such information is available, the assignment becomes easier. Two applications are presented for illustrations.
Key words and phrases: Orthogonal arrays, Hadamard product, replacement, level changes, trend resistance.