Abstract: This paper explores the role of one-at-a-time experimentation in parameter design of engineering systems. The focus is on degree of improvement achieved rather than on efficiency in estimating model parameters. The performance of adaptive one-at-a-time plans is compared with the performance of orthogonal arrays through computer simulations based on data from 66 response variables in 27 full factorial experiments described in science and engineering journals and textbooks. From the simulation results, a map of the expected gains in performance is provided as a function of the degree of pure experimental error and the strength of interactions among experimental factors. When experimental error is small (less than a quarter of the factor effects) or the interactions among control factors are large (more than one-quarter of all factor effects), an adaptive one-at-a-time strategy tends to achieve greater gains than those provided by orthogonal arrays.

Abstract: Space-time block codes from orthogonal designs recently proposed by Alamouti, and Tarokh-Jafarkhani-Calderbank have attracted considerable attention due to the fast maximum-likelihood (ML) decoding and the full diversity. There are two classes of space-time block codes from orthogonal designs. One class consists of those from real orthogonal designs for real signal constellations which have been well developed in the mathematics literature. The other class consists of those from complex orthogonal designs for complex constellations for high data rates, which are not well developed as the real orthogonal designs. Since orthogonal designs can be traced back to decades, if not centuries, ago and have recently invoked considerable interests in multi-antenna wireless communications, one of the goals of this paper is to provide a tutorial on both historical and most recent results on complex orthogonal designs. For space-time block codes from both real and (generalized) complex orthogonal designs (GCODs) with or without linear processing, Tarokh, Jafarkhani and Calderbank showed that their rates cannot be greater than 1. While the maximum rate 1 can be reached for real orthogonal designs for any number of transmit antennas from the Hurwitz–Radon constructive theory, Liang and Xia recently showed that rate 1 for the GCODs (square or non-square size) with linear processing is not reachable for more than two transmit antennas. For GCODs of square size, the designs with the maximum rates have been known, which are related to the Hurwitz theorem. In this paper, We briefly review these results and give a simple and intuitive interpretation of the realization. For GCODs without linear processing (square or non-square size), we prove that the rates cannot be greater than 3/4 for more than two transmit antennas.

Abstract: The use of optimal orthogonal array latin hypercube designs is proposed. Orthogonal arrays were proposed for constructing latin hypercube designs by Tang (1993). Such designs generally have better space filling properties than random latin hypercube designs. Even so, these designs do not necessarily fill the space particularly well. As a result, we consider orthogonal-array-based latin hypercube designs that try to achieve optimality in some sense. Optimization is performed by adapting strategies found in Morris & Mitchell (1995) and Ye et al. (2000). The strategies here search only orthogonal-array-based latin hypercube designs and, as a result, optimal designs are found in a more efficient fashion. The designs found are in general agreement with existing optimal designs reported elsewhere.

Abstract: In this chapter and the next, we discuss how to select inputs at which to compute the output of a computer experiment to achieve specific goals. The inputs we select constitute our “experimental design.” The region corresponding to the values of the inputs over which we wish to study or model the response is the experimental region. A point in this region corresponds to a specific set of values of the inputs. Thus, an experimental design is a specification of points in the experimental region at which we wish to compute the response.

Abstract: In this paper, we generalize the known topology-transparent medium access control protocols for mobile ad hoc networks by observing that their transmission schedule corresponds to an orthogonal array. Some new results on throughput are obtained as a consequence. We also show how to compute the probability of successful transmission if the actual node degree in the network exceeds the design parameter related to maximum node degree, showing the sensitivity of the schedule to this parameter. The selection of orthogonal array to provide the best throughput is also examined, and combinatorial generalizations are explored. Finally we outline schemes that combine the delay guarantees of current approaches to handle exceeding the stipulated maximum node degree.

Abstract: In factor screening, often only a few factors among a large pool of potential factors are active. Under such assumption of effect sparsity, in choosing a design for factor screening, it is important to consider projections of the design onto small subsets of factors. Cheng showed that as long as the run size of a two-level orthogonal array of strength two is not a multiple of 8, its projection onto any four factors allows the estimation of all the main effects and two-factor interactions when the higher-order interactions are negligible. This result applies, for example, to all Plackett-Burman designs whose run sizes are not multiples of 8. It is shown here that the same hidden projection property also holds for Paley designs of sizes greater than 8, even when their run sizes are multiples of 8. A key result is that such designs do not have defining words of length three or four. Applications of this result to the construction of $E(s^2)$-optimal supersaturated designs are also discussed. In particular, certain designs constructed by using Wu's method are shown to be $E(s^2)$-optimal. The article concludes with some three-level designs with good projection properties.

Abstract: We consider two related models for interference: one having different directional neighbour effects and one with the same neighbour effects. We show that optimal designs for one model can be obtained from optimal designs for the other model.

Abstract: Two new constructions of complex orthogonal space-time block codes of order 8 based on the theory of amicable orthogonal designs are presented and their performance compared with that of the standard code of order 8. These new codes are suitable for multi-modulation schemes where the performance can be sacrificed for a higher throughput. Category: Information Theory, Communication

Abstract: Publisher Summary Experimenters utilize fractional factorial designs to study the most important factors or process/design parameters that influence critical quality characteristics. Fractional factorial experiments are used for pilot studies and screening experiments where the goal is to gain the maximum information about a process in a limited number of experimental trials. This chapter provides details for constructing fractional factorial experiments and highlighting the problems associated with highly fractionated factorial experiments wherein main effects are confounded or aliased with two-order interactions. Fractional factorial design is a type of orthogonal array design that allows experimenters to study main effects and desired interaction effects in a minimum number of trials. These fractional factorial designs are the most widely and commonly used types of design in industry. Extensive graphical tools have been used through the use of real-world examples in manufacturing industry.

Abstract: A statistical experiment limited by practical constraints may have to be conducted with less than the number of runs required in a regular orthogonal array. When this is anticipated, a design matrix which is a submatrix of an orthogonal array may be constructed in a way that still permits useful estimation of a reduced number of effects. In this paper, the procedure for this design construction is proposed for two-level experiments, taking into account both the feasibility and efficiency of the resulting design.

Abstract: The use of Taguchi methods and multiple regression analysis for the development of a melting process using an optimal high energy electron beam (HEEB) melting process to produce high hardness in metals is presented. The HEEB case hardening process was carried out on ductile and flake cast iron. The processing parameters studied included the substrate material matrix, travel speed, accelerating voltage, electrical current, melted width, beam oscillation, and post-heat treatment temperature. In this study, an L18 orthogonal array was introduced for experimental designs and tests. The 'larger the better' criterion for the signal to noise ratios was used as a quality characteristic to evaluate the experimental results. Multiple regression analysis demonstrated better accuracy for forecasting the micro-hardness value of the HEEB melted specimens than the Taguchi methods. The first generated an average error of 3.867% from predicted values, whereas the latter produced an average error of 8.953%. The exp...

Abstract: Design of experiments is a tool for product and process design whose application can lead to an understanding of the complex relationship between input parameters and the output. After a great deal of time spent constructing and studying layouts for imp..

Abstract: This paper attempts to explain the empirically demonstrated phenomena that, under some conditions, one-at-a-time experiments outperform orthogonal arrays (on average) in parameter design of engineering systems. Five case studies are presented, each based on data from previously published full factorial experiments on actual engineering systems. Computer simulations of adaptive one-at-a-time plans and orthogonal arrays were carried out with varying degrees of pseudo-random error added to the data. The average outcomes are plotted for both approaches to optimization. For each of the five case studies, the main effects and interactions of the experimental factors are presented and analyzed to explain the observed simulation results. It is shown that, for some types of engineering systems, “one-at-a-time” designs consistently exploit interactions despite the fact that these designs lack the resolution to estimate interactions. It is also confirmed that orthogonal arrays are adversely affected by confounding of main effects and interactions.Copyright © 2003 by ASME

Abstract: A critical set is a partial Latin square that has a unique completion to a Latin square, and is minimal in this property. Suppose that P is a critical set in a Latin square L of order n, and there is one row of P which is empty. Then there are at most two rows of P with precisely one entry, and thus |P| ≥ 2n - 4. Moreover, in this case these three rows in L are isotopic to three adjacent rows in the back circulant Latin square. In our proof new algorithms for constructing Latin trades in arbitrary Latin squares are given.

Abstract: A design method with consecutive orthogonal arrays is implemented on dimensioning the LC filters in the diode-bridge rectifier for improving the input power quality. The power factor and the total harmonic distortion are assigned as the observational outputs of orthogonal arrays. The average effects are used as indices to arrange the following orthogonal array in accordance with the inferential rules. The implementation of the design method is illustrated by a design example. With much fewer calculations, the desired component values of the LC filter can be found by manipulating a series of consecutive orthogonal arrays.

Abstract: . This paper presents a novel genetic algorithm for analog module placement. It is based on a generalization of the two-dimensional bin packing problem. The genetic encoding and operators assures that all constraints of the problem are always satisfied. Thus the potential problems of adding penalty terms to the cost function are eliminated, so that the search configuration space decreases drastically. The dedicated cost function covers the special requirements of analog integrated circuits. A fractional factorial experiment was conducted using an orthogonal array to study the algorithm parameters. A meta-GA was applied to determine the optimal parameter values. The algorithm has been tested with several local benchmark circuits. The experimental results show this promising algorithm makes the better performance than simulated annealing approach with the satisfactory results comparable to manual placement.

Abstract: Surface finish in end milling depends upon a number of variables, such as feed rate, cutting speed, tool material, etc. The relative effect of these variables on surface roughness is not understood very well. The Taguchi method is used in end milling process to identify variables having major influence on surface finish. Partial factorial design using L9 orthogonal array is used in the design of experiments. Signal to Noise ratio analysis along with analysis of variance is used to study the effect of these parameters on surface finish. Knowledge about these relationships will help a process planner or a machinist optimize the cutting process with respect to surface finish.Copyright © 2003 by ASME

Abstract: A method for generating a memory of various sizes and configurations uses a plurality of banks. The banks are selected to meet memory requirements and size constraints and are arranged in an orthogonal array. Critical paths are minimized using commercially available software.

Abstract: 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 (2001). Optimal supersaturated designs are shown to have a periodic property and general methods for constructing optimal multilevel supersaturated designs are proposed. Inspired by the Addelman-Kempthorne construction of orthogonal arrays, optimal multi-level supersaturated designs are given in an 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.

Abstract: This paper describes the application of a combined orthogonal array design and overlapping resolution mapping to the optimization of miceller electrokinetic chromatography for the separation of 10 substituted benzenes. The most important factors were first determined according to an OA16(215) through 16 pre-designed experiments; a second set of experiments was carried out according to a triangle overlapping resolution mapping scheme, in which 7 pre-planed experiments were executed and global optimum conditions for the separation were obtained.

Abstract: Two ways of constructing maximal sets of mutually orthogonal Latin squares are presented. The first construction uses maximal partial spreads in PG(3, 4) b PG(3, 2) with r lines, where r ∈ l6, 7r, to construct transversal-free translation nets of order 16 and degree r + 3 and hence maximal sets of r + 1 mutually orthogonal Latin squares of order 16. Thus sets of t MAXMOLS(16) are obtained for two previously open cases, namely for t e 7 and t e 8. The second one uses the (non)existence of spreads and ovoids of hyperbolic quadrics Q+ (2m + 1, q), and yields infinite classes of q2n − 1 − 1 MAXMOLS(q2n), for n ≥ 2 and q a power of two, and for n e 2 and q a power of three.