An effective step-down algorithm for the construction and the identification of nonisomorphic orthogonal arrays

In this paper we present an effective algorithm for the construction and the identification of two-level nonisomorphic orthogonal arrays. Using this algorithm, we identify and list a full catalogue of nonisomorphic orthogonal arrays with parameters OA(24,7,2,t), OA(28,6,2,t) and OA(32,6,2,t), t ≥ 2. Some statistical properties of these designs are also considered.     

Projection properties of certain three level orthogonal arrays

Two orthogonal arrays based on 3 symbols are said to be isomorphic or combinatorially equivalent if one can be obtained from the other by a sequence of row permutations, column permutations and permutations of symbols in each column. Orthogonal arrays are used as screening designs to identify active main effects, after which the properties of the subdesign for estimating these effects and possibly their interactions become important. Such a subdesign is known as a ``projection design'. In this paper we have identified all the inequivalent projection designs of an OA(27,13,3,2), an OA(18,7,3,2) and an OA(36,13,3,2) into k=3,4 and 5 factors. It is shown that the generalized wordlength pattern criterion proposed by Ma and Fang [23] can distinguish between most, but not all, inequivalent classes. We propose an extension of the Es² criterion (which is commonly used for measuring efficiency of 2-level designs) to distinguish further between the non-isomorphic classes and to measure the efficiency of the designs in these classes. Some concepts on generalized resolution are also discussed.     

A new approach in constructing orthogonal and nearly orthogonal arrays

Orthogonal arrays have been constructed by a number of mathematical tools such as orthogonal Latin squares, Hadamard matrices, group theory and finite fields. Wang and Wu (1992) proposed the concept of a nearly orthogonal array and found a number of such arrays with high efficiency. In this paper we propose some criteria for non-orthogonality and two algorithms for the construction of orthogonal and nearly orthogonal arrays evincing higher efficiency than that obtained by Wang and Wu. Received: September 1999     

Some orthogonal arrays with 32 runs and their projection properties

Screening designs are useful for situations where a large number of factors are examined but only a few, k, of them are expected to be important. Traditionally orthogonal arrays such as Hadamard matrices and Plackett Burman designs have been studied for this purpose. It is therefore of practical interest for a given k to know all the classes of inequivalent projections of the design into the k dimensions that have certain statistical properties. In this paper we present 15 inequivalent Hadamard matrices of order n=32 constructed from circulant cores. We study their projection properties using several well-known statistical criteria and we provide minimum generalized aberration 2 level designs with 32 runs and up to seven factors that are embedded into these Hadamard matrices. A concept of generalized projectivity and design selection of such designs is also discussed.AMS Subject Classification: Primary 62K15, Secondary 05B20     

Projection Properties of Hadamard Matrices of Order 36 Obtained from Paley’s Constructions

In this paper we study the projection properties of 12 inequivalent Hadamard matrices of order 36 obtained from Paley’s constructions, using several statistical criteria. We also present generalized minimum aberration designs with 36 runs and up to 7 columns that are embedded into these Hadamard matrices.