A novel combinatorial criterion, called minimum moment aberration, is proposed for assessing the goodness of nonregular designs and supersaturated designs. The new criterion, which is to sequentially minimize the power moments of the number of coincidences among runs, is a surrogate with tremendous computational advantages for many statistically justified criteria, such as minimum G 2 -aberration, generalized minimum aberration and E(s ). In addition, the minimum moment aberration is conceptually simple and convenient for theoretical development.

ii Testing is an expensive but essential part of any software project. Having the right methods to detect faults is a primary factor for success in the software industry. Component based systems are problematic because they are prone to unexpected interaction faults, yet these may be left undetected by traditional testing techniques. In all but the smallest of systems, it is not possible to test every component inter-action. One can use a reduced test suite that guarantees to include a defined subset of interactions instead. A well studied combinatorial object, the covering array, can be used to achieve this goal. Constructing covering arrays for a specific software system is not always simple and the resulting object may not closely mirror the real test environment. Not only are new methods for building covering arrays needed, but new tools to support these are required as well. Our aim is to develop methods for building smaller test suites that provide stronger interaction coverage, while retaining the

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A supersaturated design is a design whose run size is not large enough for estimating all the main effects. The goodness of multi-level supersaturated designs can be judged by the generalized minimum aberration criterion proposed by Xu and Wu [Ann. Statist. 29 (2001) 1066–1077]. A new lower bound is derived and general construction methods are proposed for multi-level supersaturated designs. Inspired by the Addelman–Kempthorne construction of orthogonal arrays, several classes of optimal multi-level supersaturated designs are given in explicit form: Columns are labeled with linear or quadratic polynomials and rows are points over a finite field. Additive characters are used to study the properties of resulting designs. Some small optimal supersaturated designs of 3, 4 and 5 levels are listed with their properties. 1. Introduction. As science and technology have advanced to a higher level, investigators are becoming more interested in and capable of studying large-scale systems. Typically these systems have many factors that can be varied during design

This report provides a list of virtually all known strength-two orthogonal arrays up through 143 runs 1 (rows or factor combinations) and a list of parent orthogonal arrays up through 513 runs. At the end of these lists is a reference list of books and papers on orthogonal array construction. While these listings are virtually complete for the smaller arrays, new arrays are being discovered all the time. The reference list mostly covers newer and larger arrays. Many of the older arrays were created based on secondary sources such as Orthogonal Fractional Factorial Designs by Dey (1985); Orthogonal Arrays by Hedayat, Sloane, and Stufken (1999); and A Library of Orthogonal Arrays, by Sloane (2005). Their reference lists are not duplicated here. If you know of any arrays that are not in this catalog or references that should be in this list, please

In this paper we define the concept of orthogonality between two factors ”through another factor”. Exploiting this property we have been able to obtain orthogonal main effect plans (OMEP) on non-orthogonal blocks requiring considerably smaller number of blocks than the existing methods. We have also constructed saturated partially orthogonal main effect plans (MEPs) for (i) an n 4.2 3 experiment and (ii) an n 4.2.3 experiment both on 4n runs. Here n is an integer ≥ 3, n ̸ = 4. As particular cases, we have been able to accomodate four six-level factors on 8 blocks of size 4 each using the first method and on 24 runs using the second. AMS Subject Classification: 62k10. Key words and phrases: main effect plans, partial orthogonality.