Abstract: In protein crystallography, the initial experimental problem is the identification of physical and chemical conditions that will support nucleation and crystal growth. Ideally, experiments to search for such conditions would be based on a full-factorial structure, with variation in the temperature and solution composition. However, consideration of even a moderate number of possibilities for the composition of the system will result in factorial experiments which may be prohibitively large. In this paper it is proposed that search experiments for protein crystallization might be based on orthogonal arrays. These are subsets of full-factorial experiments which possess a great deal of symmetry, such that a uniform distribution of points throughout the experimental region is preserved. Such experiments have reasonable size, explore the proposed experimental region in a systematic fashion, and form a logical basis for a sequential approach to the search for crystallization conditions. Examples of such initial search experiments are given, and their application to some recent protein crystallization problems in this laboratory is described briefly. The relationship of this approach to other protein crystallization search procedures is also discussed.

Abstract: This paper introduces an experimental solution for H weighting function selection by exploiting an experimental planning method that has been used in quality control. Conducting matrix experiments using special matrices, called orthogonal arrays, allows the effects of several weighting parameters to be determined efficiently so that the resulting H* controller can satisfy many design specifications simultaneously in the environment for which the controller is designed. To show the feasibility and efficiency of this methodology, a flight control system for an airplane is designed to satisfy 11 performance specifications simultaneously, when the airplane is undergoing a large shift in c.g. position.

Abstract: A scheme for an application of the Taguchi method is suggested as a post process of the conventional structural optimization Design variables of the optimization are substituted by the factors of the Taguchi method If an optimum solution is calculated in the continuous space of design variables, an orthogonal array is constructed by the neighboring values of the optimum solution The neighboring values are determined form the available sizes in the design specifications which have discrete values By evaluating the orthogonal array and SN ratio, the final design is determined Unconstrained and constrained problems are solved for application examples

Abstract: Graph-aided methods for accommodating the estimation of interactions in factorial experiments have become popular among industrial users. Notable among them is the method of linear graphs due to Taguchi. Previously, some shortcomings of Taguchi's linear..

Abstract: Taguchi1 has provided 18 orthogonal arrays which have been widely touted as useful frameworks for planning experiments. Thirteen of these are ‘saturated designs’, that is, they are appropriate for investigating (N - 1) factors in N runs, thus using the full capacity of the design. Here, the other five ‘non-saturated’ designs are discussed. By creating additional, orthogonal columns which provide estimates of interaction effects, we can essentially wring out some additional information over and above that suggested by Taguchi, without additional cost. In particular, if only the linear effect is of interest for any specific factor, one can accommodate more factors than the number suggested by Taguchi. An example is given for illustration.

Abstract: A new algorithm has been developed which deals with the problem of least cost tolerance allocation with process selection. This algorithm uses the combinatorial nature of orthogonal arrays and experimental optimization techniques to allocate the magnitude of tolerance to each design dimension and select the corresponding manufacturing process. Interaction graphs are used to assign the dimensional tolerances to various orthogonal array structures. The proposed algorithm is capable of dealing with continuous and discrete cost functions as well as linear, nonlinear and multi-loop assembly functional requirements. Several examples are used to illustrate the effectiveness of the developed technique. Results indicate the superiority of the developed algorithm with those obtained using discrete, combinatorial, combined discrete and continuous and sequential quadratic programming. >

Abstract: Orthogonal arrays (OAs) are basic combinatorial structures, which appear under various disguises in cryptology and the theory of algorithms. Among their applications are resilient and correlation-immune functions, derandomization of algorithms, random pattern testing of VLSI chips, authentication codes, universal hash functions, threshold schemes, and perfect local randomisers. This dissertation is a study of correlation-immune and resilient functions from a combinatorial point of view, emphasizing their connections to orthogonal arrays. An (n,m,t) resilient function is a function from n variables to m variables such that every possible output m-tuple is equally likely to occur when the values of t arbitrary inputs are fixed by an opponent and the remaining $n-t$ input variables are chosen independently at random. We provide three characterizations of non-binary correlation-immune and resilient functions; one in terms of the structure of certain associated matrix, one using Fourier transforms, and one based on orthogonal arrays. New bounds on orthogonal arrays and resilient functions are developed using Delsarte's linear programming technique. Several methods of construction of resilient functions are presented. Some of these methods of construction use linear and non-linear codes; the rest are constructions of new resilient functions from old. A table of bounds for resilient functions is also presented. New explicit bounds on orthogonal arrays and resilient functions are derived as corollaries of the linear programming technique and these bounds are shown to be as powerful as the linear programming bound itself for many parametric situations. The duality between the bounds on codes and the bounds on orthogonal arrays is studied. Also, several classes of optimal resilient functions are constructed. The constructions involve MDS codes, perfect codes and the theory of anticodes. A conjecture of Chor et al concerning symmetric resilient functions is disproved by construction of an infinite class of counterexamples. A short proof of a recent result by Lloyd concerning the non-existence of certain cryptographic functions is also presented.

Abstract: An (r,λ)-design with mutually balanced nested subdesigns (for brevity, (r,λ)-design with MBN) is introduced firstly in this article. It is shown that an r,λ-design with MBN is equivalent to a balanced array of strength 2 with s symbols. By the use of a nested design and an orthogonal array, a construction of an r,λ-design with MBN is given. A direct construction of such an (r,λ)-design, based on the result obtained by Wilson [15], is also given. By these constructions, new balanced arrays with s ≥ 3 are presented. © 1994 John Wiley & Sons, Inc.

Abstract: Every orthogonal array of strength s and of prime-power (or perhaps infinite) order q, has a well-defined collection of ranks r. Having rank r means that it can be constructed as a cone cut by qs hyperplanes in projective space of dimension r over a field of order q.

Abstract: Taguchi and Wu introduced the method of linear graphs to accommodate prespecified interaction effects in orthogonal arrays. However, it has been known for some time that Taguchi's method when applied to two-level fractional factorial designs often leads..

Abstract: This paper proposes an experimental solution for H{infinity} weighting functions selection by exploiting an experimental planning method which is widely used in quality control. Conducting matrix experiments via orthogonal array, several parameters in H{sub {infinity}} weighting functions can be determined efficiently so that the resulting controller is able to satisfy all design specifications. Of great importance, the proposed experimental method provides additional robust performance property to conventional H{sub {infinity}} control which can only prove robust stability and nominal performance. Velocity controller design of DC servomotors is demonstrated to show the remarkable robustness and superior servo performance provided by experimental H{sub {infinity}} design. A hardware environment is constructed to correlate the theoretical prediction and the measurement data. All specifications of robust stability and performance are validated by the experimental results.

Abstract: This article presents an experimental optimization of the noise figure of small-signal self-aligned FETs. An L18 orthogonal array has been used to find the main effects of specific device parameters on noise performance at 18 GHz. This knowledge has been used to find an alternative device which shows a ∼0.7-dB improvement in noise measure without requiring major process changes. Hybrid low-noise amplifiers built with the improved FETs confirm the noise performance and show record power performance for high dynamic range applications. © 1994 John Wiley & Sons, Inc.

Abstract: Summary form only given. An account is given of recent work by the author and his colleagues on the application of techniques from error-correcting codes to the design of experiments. >

Abstract: A new algorithm for form tolerance evaluation has been developed. Evaluation of the minimum tolerance zone is formulated as an optimization problem following the definitions of geometric tolerances in the current ANSI standards. The algorithm utilizes the experimental optimization techniques and the combinatorial nature of orthogonal arrays to plan the experimentation and evaluate the minimum tolerance zone. The approach is applied to 2-dimensional features tolerances such as straightness and circularity (roundness) and 3-dimensional features such as flatness. The obtained results are compared with other approaches using the least square method the constrained optimization techniques and the convex hull approach. >

Abstract: Orthogonal arrays (OAs) are basic combinatorial structures, which appear under various disguises in cryptology and the theory of algorithms. Among their applications are universal hashing, authentica- tion codes, resilient and correlation-immune functions, derandomization of algorithms, and perfect local randomizers. In this paper, we give new bounds on the size of orthogonal arrays using Delsarte's linear program- ming method. Then we derive bounds on resilient functions and discuss when these bounds can be met.

Abstract: The theory and methodology of two-level orthogonal array design for the optimization of analytical procedures were developed. In the theoretical part, the matrix of the two-level orthogonal array design is described while orthogonality is proved by a linear regression model. Then, the assignment of experiments in a two-level orthogonal array design and the application of the triangular table associated with the corresponding orthogonal array matrix are illustrated, followed by the data analysis strategy, in which significance of the different factor effects is quantitatively evaluated by the analysis of variance (ANOVA) technique and the percentage contribution method. Finally, a linear regression equation representing the response surface is established to estimate the factors that have a significant influence. In the application section, microwave dissolution for the determination of selenium in biological samples by hydride generation atomic absorption spectrometry as a practical example is employed to demonstrate the application of the proposed two-level orthogonal array design in analytical chemistry.

Abstract: Using the tools of algebraic coding theory, we give a new proof of the nonexistence of two mutually orthogonal Latin squares of order 6.

Abstract: Orthogonal arrays (OAs) are basic combinatorial structures, which appear under various disguises in cryptology and the theory of algorithms Among their applications are universal hashing, authentication codes, resilient and correlation-immune functions, derandomization of algorithms, and perfect local randomizers In this paper, we give new bounds on the size of orthogonal arrays using Delsarte's linear programming method Then we derive bounds on resilient functions and discuss when these bounds can be met

Abstract: Randomized orthogonal arrays provide good sets of input points for exploration of computer programs and for Monte Carlo integration. In 1954, Patterson gave a formula for the randomization variance of the sample mean of a function evaluated at the points of an orthogonal array. That formula is incorrect for most of the arrays that are practical for computer experiments. In this paper we correct Patterson's formula. We also remark on a defect, related to coincidences, in some orthogonal arrays. These are arrays of the form $OA(2q^2, 2q + 1, q, 2)$, where $q$ is a prime power, obtained by constructions due to Bose and Bush and to Addelman and Kempthorne. We conjecture that subarrays of the form $OA(2q^2, 2q, q, 2)$ may be constructed to avoid this defect.

Abstract: The maximin distance criterion is used for the selection of an OA-based Latin hypercube. For the case in which the underlying orthogonal array is a full factorial design without replication, we construct an OA-based Latin hypercube that reaches the same distance as its parent array.