H. Evangelaras

Nonparametric Testing for Main Effects on Inequivalent Designs

A class of inequivalent orthogonal designs is considered and the aim is to provide a “permutation” test for active effects. Rather than permuting responses of a single observed design matrix (or, equivalently, permuting rows of the design matrix keeping the responses fixed), matrices are exchanged in order to obtain the permutation distribution. Such test called IMPT (Inequivalent Matrices Permutation Test) behaves well both under the null hypothesis and in power, even with heavy-tailed distributions. A comparative simulation study with Lenth’s and the parametric F-test is also presented, showing a better performance of the IMPT with respect to both other tests in the case of Cauchy errors distribution and a similar performance with the F-test with normal error distribution.

Projection Properties of Certain Three-Level Main Effect Plans with Quantitative Factors

ABSTRACT 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 article, we have identified all the geometric non isomorphic 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 when they are used for screening out active quantitative experimental factors, with regard to the prior selection of the middle level of factors. We use the popular D-efficiency criterion to evaluate the ability of each design found in estimating the parameters of a second order model.

Another Look at Projection Properties of Hadamard Matrices

Abstract Suppose a large number of factors (q) is examined in an experimental situation. It is often anticipated that only a few (k) of these will be important. Usually, it is not known which of the q factors will be the important ones, that is, it is not known which k columns of the experimental design will be of further interest. Screening designs are useful for such situations. It is 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, since it helps experimenters in selecting a screening design with favorable properties. In this paper we study all the classes of inequivalent projections of certain two-level orthogonal arrays that arise from Hadamard matrices, using well known statistical criteria, such as generalized resolution and generalized minimum aberration. We also pay attention to each projections distinct runs. Results are given for orthogonal arrays with n = 16, 20 and 24 runs, when they are projected into small dimensions. Useful remarks on design selection are made based on the frequency of appearance of each projection design in every Hadamard matrix.

Combined Arrays with Minimum Number of Runs and Maximum Estimation Efficiency

Abstract Robust parameter design, originally proposed by Taguchi [Taguchi, G. (1987). System of Experimental Design. Vol. I and II. New York: UNIPUB], is an off-line production technique for reducing variation and improving products quality by using the product arrays. However, the use of the product arrays results in an exorbitant number of runs. To overcome the drawbacks of the product array several scientists proposed the use of combined arrays, where the control and noise factors are combined in a single array.

On maximizing a design estimation efficiency using hidden projection properties

Hadamard matrices have traditionally been used for screening main effects only, because of their complex aliasing structures. The hidden projection property, as introduced by Wang and Wu (Statistica Sinica 5 (1995) 235-250), suggests that complex aliasing allows some interactions to be entertained and estimated without making additional runs in order to form full or fractional factorial designs as the geometric approach inclines. However, in most cases, because the original data are sufficiently noisy to mask the significance of any two-factor interaction we need to add (fewer) runs that give the maximum amount of information for this purpose. In this paper, we list what runs give the maximum amount of information needed in order to entertain and estimate some two-factor interactions for all the inequivalent projections of Hadamard matrices of order n=16,20 and 24 when they are projected into four and five dimensions.