Abstract: SUMMARY Latin hypercube designs are often used in computer experiments as they ensure that few design points are redundant when there is effect sparsity. In this paper, designs suitable for factor screening are presented and they are shown to be efficient in terms of runs required per factor as well as having optimal and orthogonal properties. Designs orthogonal under full second-order models are also constructed.

Abstract: In this paper we consider the utilization of multiple transmitter and receiver antennas for space-time diversity. The optimal SNR scheme, which also provides the best diversity, is outlined. This scheme however involves a reduction in the data rate. Coding schemes are then presented which not only achieve the optimal SNR but also mitigate the reduction of data rate. The proposed schemes are based on the theory of Orthogonal Designs and Amicable Orthogonal Designs.

Abstract: The objective of this research is to improve the quality of the KrF excimer laser micromachining of metal and silicon in fabricating electro-thermal-compliant (ETC) micro devices. The ETC devices combine the actuator and the mechanism into one monolithic compliant continuum and enable a range of mechanical manipulation tasks at micron scale. An efficient method for optimizing the process parameters in laser micromachining, using the orthogonal array-based experimental design method, is presented in this paper. The feed rate of the XY stage, the laser pulse frequency, the discharge voltage and the number of passes were used as the control parameters. The roughness of the machined edge was used as the primary indicator of cutting performance. The roughness of the edges was computed automatically from the optical image of the machined samples. The heat-affected zone, kerf width and rate of cutting depth (depth per one pass) were used as additional quality indicators. The orthogonal array method enabled the optimization of the control parameters by reducing the required number of experiments compared to the traditional full factorial experiment. Furthermore, machining in a liquid environment improved the quality and eliminated more debris and recast compared to machining in the air.

Abstract: A two level orthogonal array design for n observations with k factors and of projectivity P provides an (n, k, P) factor screen for which every projection into P space produces a complete 2 P factorial, possibly with certain points replicated. Box and Tyssedal [1] rigorously investigated the screening properties of such designs derived from fractional factorials and Plackett Burman orthogonal arrays (OA's). For example, they showed that these always provided (12, 11, 3) and (20, 19, 3) screens, but for 16 runs only a (16, 8, 3) screen could be generated. In this paper it is shown that designs derived from a different class of OA's due to Hall [2] can produce sixteen run designs that can screen a larger number of factors and that in particular (16, 12, 3) screens and also a (16, 14, 3) screen can be obtained.

Abstract: In this paper, two new direct construction methods are given for holey self-orthogonal Latin squares with a symmetric orthogonal mate (HSOLSSOMs). Some new HSOLSSOMs using already known methods are also given. The known existence results for HSOLSSOMs of types 1mu1 and hn are improved; for type 1mu1 there remain just four possible exceptions with u odd and 3 ≤ u ≤ 15; for type hn, there are just two possible exceptions remaining, for (h, n) = (6, 12) and (6, 18). As a byproduct, the known existence results for three holey mutually orthogonal Latin squares (3 HMOLS) are also improved. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 435–444, 2001

Abstract: A multivariate orthogonal regression method is presented for analyzing data from orthogonal array experiments. The least squares method is used to fit data with an orthogonal polynomial regression model to obtain the same statistical test results as..

Abstract: This study presents an air-bearing design procedure by using Taguchi's Design of Experiments (TDE) to simulate the analysis of systems without adequate models. Instead of taking data from experiments, the performance of air bearings is obtained by an empirical verified numerical model. This arrangement eliminates the errors inevitably introduced in tests. When comparing with full factorial analysis, the number of tests is significantly reduced by using TDE in the demonstrated study. The optimum set of the variables predicted by TDE is numerically verified in the cases investigated. The analysis of orthogonal arrays consisting of three levels shows better performance prediction than the two levels analysis. The straightforward and easy to use procedure can be applied conjunction with numerical optimization technique to give an excellent start-point to minimize search time in a multi-variable design as illustrated in this report. Presented as a Society of Tribologists and Lubrication Engineers Paper at the ...

Abstract: The structural optimization have been carried out in the continuous design space or in the discrete design space. Methods fur discrete variables such as genetic algorithms , are extremely expensive in computational cost. In this research, an iterative optimization algorithm using orthogonal arrays is developed for design in discrete space. An orthogonal array is selected on a discrete des inn space and levels are selected from candidate values. Matrix experiments with the orthogonal array are conducted. New results of matrix experiments are obtained with penalty functions leer constraints. A new design is determined from analysis of means(ANOM). An orthogonal array is defined around the new values and matrix experiments are conducted. The final optimum design is found from iterative process. The suggested algorithm has been applied to various problems such as truss and frame type structures. The results are compared with those from a genetic algorithm and discussed.

Abstract: Our work deals with ATM satellite communications networks employing DAMA, whose algorithm must be efficient and robust. Its efficiency ensures a fast response to a connection's demand for bandwidth. Its robustness ensures satisfaction of the connection's required QoS and its integrity under unpredictable traffic burstiness. Computational practicality dictates that only heuristic DAMA algorithms be implemented in an ATM satellite communications system. But these heuristic algorithms need be validated and benchmarked before they are fielded. In this work, we employ the orthogonal array experiment (or the Taguchi method) to allocate bandwidth in a satellite communications network. We also validate and benchmark the Taguchi assignments with the results obtained by mathematical optimization. This benchmarking process allows us to quantitatively assess the performance of our approach and is recommended to be employed when developing heuristic algorithms. The close agreement between the results produced by the orthogonal array experiment method and the conventional integer programming solution methods underscores the feasibility of the orthogonal array experiment approach.

Abstract: An efficient design method for flip chip ball grid array (BGA) packages has been developed. This method uses design of experiment (DOE), a series of finite element (FE) stress analyses based on an orthogonal array used in DOE, and statistical analysis. By using this method to design a BGA package having 1600 pins, the warpage of the optimum packaging structure is very small and all of the reliability demands are satisfied.

Abstract: Since 1782, when Euler addressed the question of existence of a pair of Orthogonal Latin Squares (OLS) by stating his famous conjecture ([8, 9, 13]), these structures have remained an active area of research due to their theoretical properties as well as their applications in a variety of fields. In the current work we consider the polyhedral aspects of OLS. In particular we establish the dimension of the OLS polytope, describe all cliques of the underlying intersection graph and categorize them into three classes. For two of these classes we show that the related inequalities have Chvatal rank two and both are facet defining. For each such class, we give a separation algorithm of the lowest possible complexity, i.e. linear in the number of variables.

Abstract: An optimization technique that expands the application of response surface methodology (RSM) of conventional design-of-experiments techniques into the utilization of the Taguchi method's orthogonal arrays is proposed to improve the efficiency of RSM. A case study of NMOS device-window check of threshold voltage is used to illustrate the implementation of this method.

Abstract: In the Taguchi parameter design, the product-array approach using orthogonal arrays is mainly used. However, it often requires an excessive number of experiments. An alternative approach, which is called the combined-array approach, was suggested by Welch et al (1990) and studied by Vining and Myers (1990) and others. In these studies, only single respouse variable was considered. We propose how to simultaneously optimize multiple responses when there are correlations among responses.

Abstract: This paper describes the approach used in a cost optimization study for a single-stage-to-orbit launch vehicle. Taguchi's experimental designs called orthogonal arrays are utilized for efficiently studying the effect of different material and technology options on design, development, test and evaluation cost. The results suggest that the approach taken facilitates rapid evaluation on a cost basis early in the design phase and may lead to reduced project costs.

Abstract: The source array manifold can be used to improve signal synthesis from the Wigner-Ville distribution (WVD). In the proposed approach, the inner products of source array vectors translate into weighting factors that reduce the crossterms between the source signals, and thus yield improved synthesis. Orthogonal array manifold vectors remove any interaction between their respective source waveforms in the time-frequency (t-f) domain. For Gaussian channel and omni-directional antennas, the spatial signature estimation and the quality of the synthesized signals impinging on a multi-antenna receiver depend on the angular separation of the sources as well as the source t-f characteristics. Evaluations of the proposed technique in terms of performance and computations are provided.

Abstract: A new fuzzy logic control design algorithm suitable for multiobjective control problems is proposed based on the orthogonal array that is widely used for design of experiments in statistics and industrial engineering. The essence of the algorithm is to introduce an n-th order certainty factor for each rule defined from its F-value, in order to effectively exclude the less confident rules and rate the rules. The proposed algorithm with multiobjective decision table (MODT) is found to be capable of detection of inconsistency and the rule classification, reduction and modification. It is also shown that the algorithm can be successfully applied to the fuzzy controller design of a rigid rotor-active magnetic bearing (AMB) system with model uncertainties.

Abstract: As the solution of the automotive frontal crashworthiness is settled, side impact problem becomes challengeable. The door stiffness is the most important factor for the side impact. Generally, researches have been conducted on the assembled door. A side impact door beam is installed in a door to protect occupants from the side impact. The research is only concentrated on the side impact beam and a side impact beam is designed. The cross section is defined to have an elliptic shape. An optimization problem is defined to minimize the weight of the structure while various constraints are satisfied. Design variables are the radii and the thickness of the ellipsoid. The analysis of the side impact is carried out by the nonlinear finite element method. The optimization problem is solved by two methods. An orthogonal array is established around the existing design. Since the radii are included in the design variable set, a finite element model is made for each row of the array. Firstly, the formulated problem is solved by an algorithm which can handle constraints with orthogonal arrays. Secondly, the response surface method (RSM) is utilized. The functions are approximated by the information from the orthogonal array. Both methods can obtain better designs than the current one.

Abstract: The NOA module of the Gendex toolkit may be used to obtain 2-level main effect plans for 2 to 128 factors, for constructing orthogonal or near-orthogonal arrays, and for constructing supersaturated fractional replicates of a complete factorial In addition, a 2level main effect plan may be augmented with single degree of freedom contrasts for a k-level factor with this module An explanation of the steps to construct a plan is given Several examples are presented to illustrate various features of the NOA module

Abstract: In this paper, using uniform design and orthogonal array we give a method of constructing lower discrepancy OA-based Latin hypercube designs. The designs constructed by this method have not only good uniformity and also orthogonality. Another advantage is that design point sets of large size can constructed. Also, this paper give some uniform design tables and these designs are better than existing uniform designs.

Abstract: This article illustrates a technique for visualizing nonlinear mappings ƒ:ℝk → ℝm that arise frequently in engineering applications. The idea is based on viewing sections ƒ−1(B) of the domain ℝk, and ƒ(A) of the range ℝm, respectively. After suitable discretization, such sections are easily approximated with familiar brushing operations in scatterplot matrices. An obvious approach to discretization is to evaluate f on a factorial grid in ℝk and view the sections by restriction to the grid and its image. The problem is that factorial grids grow large quickly for desirable numbers of grid points (knots) and even moderate dimensions k. The problem can be solved by thinning factorial grids using techniques familiar from experimental design: orthogonal arrays constructed from sets of orthogonal Latin squares. As a result, one obtains manageable sets of domain points with desirable visual properties, high density in each variable pair, and the ability to capture pairwise variable interactions in ƒ. The benefits...

Abstract: Non-regular factorial designs have not been advocated until last decade clue to their complex aliasing structure. However, some researchers recently found that the complex aliasing structure of non-regular factorial designs is a challenge as well as an opportunity. Li, Deng, and Tang (2000) studied nOll-regular designs and generated a collection of non-equivalent orthogonal arrays using a generalized miniumm aberration criterion, proposed by Deng and Tang (1999). Some new orthogonal arrays they found cannot be embedded into Hadamard matrices. In this paper, we study these orthogonal arrays from the angle of projection. vVe show that these new GMA orthogonal arrays are also superior to the top designs obtained from Hadamard matrices when evaluated hy the criteria of model estimability and design efhc:ienc:y. }(e:1J WOTYiS and phmses: non-regular design, gcncrajizccl minimum aberratiun, model cstimaIJility, design efficiency, Hadamard matrices, orthogona.l alTays. Conference on Applied Statistics in Agriculture Kansas State University New Prairie Press https://newprairiepress.org/agstatconference/2001/proceedings/10 Applied Statistics in Agriculture 117

Abstract: An alternative analysis method to the conventional analysis of variance is proposed for the problem of identifying the active factors in pk unreplicated fractional factorial experiments (orthogonal arrays). The sums of squares calculated are arranged in ascending order, as S(1)≤S(2)≤S(3) ≤…≤ S(n). Assuming the least sum of squares, S(1) is inactive, i.e. having zero effect, the next candidate of inactive sums of squares, S(2), is tested. The following sums of squares, S(i)’s, i = 3,…, n, are tested by the pooled inactive sums of squares, on the condition that S(2),…, S(i-1) are not significant at the preceding tests, successively. The significance level of each test, as is set the same value and the overall risk of the first kind of the whole procedure, aT, is controlled to be 1%, 5% or 10%. The critical values at each step is numerically obtained for 33 orthogonal designs, and empirically obtained for 24 orthogonal designs by the Monte Carlo method. The proposed method can be applied not only to 2k, 31` orthogonal designs but also to Plackett-Burman designs.

Abstract: The application of Hadamard matrices to the theory and construction of experimental designs is of considerable importance. The purpose of this study is to point out some connections between Hadamard matrices, bal- anced incomplete block designs(BIB designs) and orthogonal arrays.