Showing papers on "Orthogonal array published in 1996"
TL;DR: Balanced Incomplete Block Designs and t-Designs2-(v,k,l) Designs of Small OrderBIBDs with Small Block Sizet-designs, t = 3Steiner SystemsSymmetric DesignsResolvable and Near Resolvable DesignsLatin Squares, MOLS, and Orthogonal ArraysLatin SquareMutually Orthogonomic Latin Squares (MOLS)Incomplete MOLsOrthogonal ARrays of Index More Than OneOrthoghonal Array of Strength More Than TwoPairwise Balanced Designs
Abstract: Balanced Incomplete Block Designs and t-Designs2-(v,k,l) Designs of Small OrderBIBDs with Small Block Sizet-Designs, t = 3Steiner SystemsSymmetric DesignsResolvable and Near Resolvable DesignsLatin Squares, MOLS, and Orthogonal ArraysLatin SquaresMutually Orthogonal Latin Squares (MOLS)Incomplete MOLSOrthogonal Arrays of Index More Than OneOrthogonal Arrays of Strength More Than TwoPairwise Balanced DesignsPBDs and GDDs: The BasicsPBDs: Recursive ConstructionsPBD-ClosurePairwise Balanced Designs as Linear SpacesPBDs and GDDs of Higher IndexPBDs, Frames, and ResolvabilityOther Combinatorial DesignsAssociation SchemesBalanced (Part) Ternary DesignsBalanced Tournament DesignsBhaskar Rao DesignsComplete Mappings and Sequencings of Finite GroupsConfigurationsCostas ArraysCoveringsCycle SystemsDifference FamiliesDifference MatricesDifference Sets: AbelianDifference Sets: NonabelianDifference Triangle SetsDirected DesignsD-Optimal MatricesEmbedding Partial QuasigroupsEquidistant Permutation ArraysFactorial DesignsFrequency SquaresGeneralized QuadranglesGraph Decompositions and DesignsGraphical DesignsHadamard Matrices and DesignsHall Triple SystemsHowell DesignsMaximal Sets of MOLSMendelsohn DesignsThe Oberwolfach ProblemOrdered Designs and Perpendicular ArraysOrthogonal DesignsOrthogonal Main Effect PlansPackingsPartial GeometriesPartially Balanced Incomplete Block DesignsQuasigroupsQuasi-Symmetric Designs(r,l)-DesignsRoom SquaresSelf-Orthogonal Latin Squares (SOLS)SOLS with a Symmetric Orthogonal Mate (SOLSSOM)Sequences with Zero AutocorrelationSkolem SequencesSpherical t-DesignsStartersTrades and Defining Sets(t,m,s)-NetsTuscan Squarest-Wise Balanced DesignsUniformly Resolvable DesignsVector Space DesignsWeighing Matrices and Conference MatricesWhist TournamentsYouden Designs, GeneralizedYouden SquaresApplicationsCodesComputer Science: Selected ApplicationsApplications of Designs to CryptographyDerandomizationOptimality and Efficiency: Comparing Block DesignsGroup TestingScheduling a TournamentWinning the LotteryRelated Mathematics and Computational MethodsFinite Groups and DesignsNumber Theory and Finite FieldsGraphs and MultigraphsFactorizations of GraphsStrongly Regular GraphsTwo-GraphsClassical GeometriesProjective Planes, NondesarguesianComputational Methods in Design TheoryIndex
2,067 citations
Book•
30 Sep 1996TL;DR: Quality engineering.
Abstract: Quality engineering. Analysis of quality information and quality improvement effort. Fundamentals of designing experiments. Orthogonal array experiments I. Orthogonal array experiments II. Parameter design for continuous data. Parameter design for discrete data. Alternative parameter design and other considerations. Parameter design for dynamic characteristics. Tolerance design. Response surface design and analysis.
555 citations
1 Jan 1996
TL;DR: Researchers investigate the arrangement of 16 playing cards in a 4x4 grid, considering constraints on suit and card type, and further explore coloring the cards with 4 colors while satisfying additional constraints on color and value.
Abstract: 1 3 Challenges 1.1 Challenge I Challenge I Consider the 16 aces, kings, queens, and jacks from a regular 52 card deck of playing card. Can the 16 cards be arranged in a 4 × 4 array so that no suit and no single kind of card occurs twice in any row or column? (The suits are spades, diamonds, hearts, and clubs.) Challenge II In addition to the above requirements, is it possible to color the cards 4 different colors (red, yellow, blue, green) such that 1. No two cards have the same color and suit, 2. No two cards have the same color and value, 3. no row or column has the same color twice?
89 citations
TL;DR: A survey of the statistical theory of orthogonal partitions on a finite set is given in this paper, which includes Latin squares, semilattices of subgroups, and partitions defined by the ancestral subsets of a partially ordered set.
Abstract: A survey is given of the statistical theory of orthogonal partitions on a finite set. Orthogonality, closure under suprema, and one trivial partition give an orthogonal decomposition of the corresponding vector space into subspaces indexed by the partitions. These conditions plus uniformity, closure under infima and the other trivial partition give association schemes. Examples covered by the theory include Latin squares, orthogonal arrays, semilattices of subgroups, and partitions defined by the ancestral subsets of a partially ordered set (the poset block structures). Isomorphism, equivalence and duality are discussed, and the automorphism groups given in some cases. Finally, the ideas are illustrated by some examples of real experiments.
65 citations
TL;DR: In this article, the convergence rate to normality of the distribution of the average of a set of f values taken from one of these designs is investigated, and it is shown that using randomized orthogonal arrays in the choice of such a set improves the convergence.
Abstract: Let X be a random vector uniformly distributed on the unit cube and $f: [0, 1]^3 \to \mathsf{R}$ be a measurable function. An objective of many computer experiments is to estimate $\mu = E(f \circ X)$ by computing f at a set of points in $[0, 1]^3$. There is a design issue in choosing these points. Recently Owen and Tang independently suggested using randomized orthogonal arrays in the choice of such a set. This paper investigates the convergence rate to normality of the distribution of the average of a set of f values taken from one of these designs.
36 citations
TL;DR: In this paper, the Delsarte theory is used to obtain a linear programming bound for orthogonal arrays with mixed levels, which is the best known bound for mixed-level arrays.
32 citations
TL;DR: In this paper, the authors discuss several useful compound designs for dispersion experiments and several general methods for constructing such designs, in particular, compound designs can be built from existing tabulations of confounded factorial designs.
Abstract: Dispersion experiments examine the effects of control factors on dispersion introduced by error factors. Error factors can be controlled in the laboratory but cannot be controlled when a product is used. For dispersion experiments, Taguchi used direct product designs in which control-factor levels are set by one orthogonal array, error-factor levels are set by another orthogonal array, and, for each combination of control-factor and error-factor levels, an observation is taken. In contrast, compound designs, which include product designs as special cases, share several of the attractive properties of Taguchi's designs, but they are often smaller for a given strength, or stronger for a given size, where strength refers to strength of the orthogonal array. This article discusses several useful compound designs for dispersion experiments and several general methods for constructing such designs. In particular, compound designs can be built from existing tabulations of confounded factorial designs.
29 citations
1 Dec 1996
TL;DR: In this article, a Direct-Inlet-Output manufacturing system (DIOMS) with a number of machine centers placed along a built-in automated storage retrieval system (AS/RS) is considered.
Abstract: Some modern manufacturing systems have workstations directly integrated with a centralized storage and handling system for work-in-process. We consider a Direct-Inlet-Output manufacturing system(DIOMS) which has a number of machine centers placed along a built-in automated storagejretrieval system(AS/RS). The storagdretrievai(S/R) machine handles parts placed on pallets for the machine centers located at either one or both sides of the AS/RS. This paper investigates the operational aspect of DIOMS by the Taguchi method. Four operating policies including input sequencing control. dispatching rule for the S/R machine, machine center-based part type selection rule, and storage assignment policy are treated as design factors. For the performance characteristics, man flow time and throughput are adopted. The number of machine centers, the number of part types, demand rate, processing time and the rate of each part type. vertical and horizontal speed of the SIR machM and the size of a local buffer in the machine centers are considered as noise factors in generating various DIOMS environments. A robust design experiment with inner and outer orthogonal arrays are conducted by computer simulation, and an optimal configuration of operating policies is presented which consists of a combination of the level of each design factor. The validity of the optimal configuration is investigated by comparing its SN ratios with those obtained by an experiment with fiill factorial designs.
27 citations
TL;DR: The proof that each element of the critical set is an essential part of the reconstruction process relies on the proof of the existence of a large number of latin interchanges.
Abstract: To date very few families of critical sets for latin squares are known. In this paper a new family of critical sets for back circulant latin squares is identified. The proof that each element of the critical set is an essential part of the reconstruction process relies on the proof of the existence of a large number of latin interchanges.
25 citations
TL;DR: In this article, a number of new incomplete transversal designs are reported, which lead to certain improved bounds on the number of mutually orthogonal latin squares, and thus to an improved number of transversals.
24 citations
TL;DR: In this paper, an orthogonal main effects plan is found by superimposing one nested row and column design upon another, and conditions are stated for statistical orthogonality of the superimposed components.
Abstract: Optimal design is studied for factorial experiments in the nested row and column setting. The approach is analogous to that of orthogonal Latin squares: main effects plans are found by the superimposition of one nested row and column design upon another. Conditions are stated for statistical orthogonality of the superimposed components, resulting in orthogonal main effects plans, and a number of constructions are given. Orthogonal collections of sets of Latin squares are introduced. All of the constructed designs are also optimal main effects plans for the row-column and the unstructured block design settings. Further applications are as optimal multidimensional incomplete block designs and as optimal designs for multistage experimentation.
TL;DR: In this paper, an application of improving process design in the metal cutting operation by the wire-cut EDM (electro discharge machining) process on a hi-tech Japax Machine was highlighted.
Abstract: Many of the quality problems have their origin either in the product design or process design. The statistical design of experiments is a scientific method for optimization of design parameters. This paper highlights an application of improving process design in the metal cutting operation by the wire-cut EDM (electro discharge machining) process on a hi-tech Japax Machine. An experiment was conducted on nine process parameters as per the L16 (215) orthogonal array layout. The responses considered were precision in machined dimensions and surface roughness. The data were then analyzed for mean and signal-to-noise ratio. All the nine factors turned out to be significant in at least one of the analyses and the best operating conditions were found considering the results of different analyses. Implementation of the results showed that the dimensional variability ( 3 sigma ) is reduced from 0.015 to 0.007 and the surface roughness from 4 mu m to 2 mu m. Other benefits were increased tool life by over 10% and ...
TL;DR: In this article, a quality improvement case of extremely thin and light chip resistor RC06 was studied using an L 18 (2 1 x 3 7 ) orthogonal array allocating eight control factors in an experimental plan.
Abstract: This paper studies a quality improvement case of extremely thin and light chip resistor RC06. We use an L 18 (2 1 x 3 7 ) orthogonal array allocating eight control factors in an experimental plan. The quality response data are inevitably considered to be ordered categorical. Six categories are classified for the quality of chips. Both Taguchi's accumulation analysis method (1966) and Nair's scoring scheme (1986) are employed in analysing the data. Furthermore, we develop a weighted probability scoring scheme (WPSS) and a signal-to-noise (SN) ratio to reach an optimal solution. Finally, a comparison among the three approaches is made.
TL;DR: In this article, the authors proposed a new practical optimum design method that consists of two steps: the design of experiments and mathematical programming, which is used to generate approximate evaluation functions for the controlling behavior depending on the changes in design variables of an object structure, by a series of finite element analyses.
Abstract: The authors proposed a new practical optimum design method that consists of two steps: the design of experiments and mathematical programming. The design of experiments is used to generate approximate evaluation functions for the controlling behavior depending on the changes in design variables of an object structure, by a series of finite element analyses (FEA). Based upon an orthogonal array of a combination of design variables, effects of the design variables can be calculated by a relatively small number of FEA, and then the approximate evaluation functions are generated by those effects based upon analysis of variance. The evaluation functions can also be used as direct tools for estimating the behavior of design structure. Finally, a successive quadratic programming (SQP) method is employed to solve the optimization problem of the approximate evaluation functions. It is confirmed that the proposed method can be used for almost all kinds of the nonlinear problems including the impact behavior of structures, and that it can be carried out in much smaller number of FEA than the other existing methods. As an example, the present method was used to solve an optimum design problem of an automobile seat frame subjected to impact loading. It was found that the present method is a very effective and powerful tool for the optimum design of various practical design problems.
Journal Article•
TL;DR: Check character systems which detect neigh-bour-transpositions or other double errors by making use of orthomorphisms or fixed point free automorphisms are described.
Abstract: In this article we describe check character systems which detect neigh-bour-transpositions or other double errors by making use of orthomorphisms or fixed point free automorphisms.
Journal Article•
TL;DR: This note gives what is believed to be the first published example of a symmetric 11 x 11 Latin square which, although not cyclic, has the property that the permutation between any two rows is an 11-cycle.
Abstract: This note gives what is believed to be the first published example of a symmetric 11 x 11 Latin square which, although not cyclic, has the property that the permutation between any two rows is an 11-cycle. The square has the further property that two subsets of its rows constitute 5 x 11 Youden squares. The note shows how this 11 x 11 Latin square can be obtained by a general construction for n x n Latin squares where n is prime with n greater than or equal to 11. The permutation between any two rows of any Latin square obtained by the general construction is an n-cycle; two subsets of (n - 1)/2 rows from the Latin square constitute Youden squares if n = 3 (mod 8).
Patent•
NEC1
TL;DR: In this paper, a set of orthonormal basis functions is determined with respect to a rectangle which includes an arbitrarily shaped image segment, and a loop for generating orthogonal basis function is initiated.
Abstract: A set of orthonormal basis functions is determined with respect to a rectangle which includes an arbitrarily shaped image segment. The set of orthonormal basis functions is used to determine a set of orthogonal basis function candidates which are numbered along a zigzag scan. Subsequently, a first orthogonal basis function candidate is extracted and defined as a first orthogonal basis function. Then, a loop for generating a set of orthogonal basis functions is initiated. First, a next basis function candidate is extracted in numbered order. An orthogonal component is determined which is perpendicular to a hyperplane spanned by the orthogonal basis function. Thereafter, a check is made as to whether an absolute value of the orthogonal component exceeds a threshold. If the absolute value does not exceed the threshold, it is disregarded and the operation returns to the beginning of the loop. On the other hand, if the absolute value exceeds the threshold, the orthogonal component is selected and defined as the next orthogonal basis function, after which the operation returns to the beginning of the loop. Alternatively, a set of orthogonal basis functions is generated by successively ascertaining a maximum orthogonal component among a plurality of orthogonal components in place of determining whether the absolute value of the orthogonal component exceeds the threshold.
TL;DR: In this paper, a method of construction of asymmetric orthogonal arrays of strength two is described, which exploits difference matrices and a special type of orthogonality.
TL;DR: In this paper, mutually orthogonal idempotent Latin squares of orders 22 and 26 are constructed, which can be used to obtain 3 HMOLS of type 522 and type 2322 and to obtain a (110, 5, 1)-PMD and a (130 5, 2)-HMOLS.
TL;DR: In this paper, a weighted A-optimality (WA) criterion is discussed for selecting a fractional 2m factorial design of resolution V, and a procedure for finding WA-optimal designs for various weights is given.
1 Sep 1996
TL;DR: In this paper, an optimization procedure was developed by coupling the finite element analysis (FEA) to the orthogonal array experimentation technique, because FEA is a common analysis tool for design engineers.
Abstract: : The objective of this research was to develop an optimization technique that can be used interactively by design engineers to approach an optimal design with minimal computational effort. The technique can be applied to both continuous and discrete values of design variables. A large number of design variables can be also considered. In order to meet the objective, an optimization procedure was developed by coupling the finite element analysis (FEA) to the orthogonal array experimentation technique, because FEA is a common analysis tool for design engineers. From the results of the FEA and an orthogonal array, an average Jacobian matrix was constructed that showed the average overall sensitivity of the design variables. These sensitivities were then used to optimize the design parameters. The process could then be repeated at the discretion of the engineer until a satisfactory design is obtained. In general, the designer can predict and control the number of FEA calculations before an optimization process so that one can plan a budget and time for an optimal design. Some examples of structural optimization with truss and frame structures with continuous and discrete values of design variables were studied using the technique developed in this paper. Their optimal solutions were found with a small number of iterations.
TL;DR: In this paper, the authors obtained orthogonal designs from Hadamard matrices and weighing matrices, respectively, in 2k and 3k factorial experiments, and used these sequences to construct some new orthogonality designs.
TL;DR: In this paper, a cyclic version of the results obtained by Kuriki and Fuji-Hara's balanced arrays with MBN is presented, which is equivalent to a balanced array of strength 2 with s symbols.
TL;DR: In this article, the Steiner triple systems are studied in the context of partial latin squares with unique completion and minimal defining sets for block designs, where the geometric structure is used to choose the blocks for the defining sets.
Abstract: This thesis is devoted to two closely related topics. These topics are critical sets in latin squares and the very similar concept, minimal defining sets for block designs. The first chapter presents the necessary background material and a view of the previous results in each of these areas. It also provides some results used in the third and fourth chapters. The second and fifth chapters are entirely devoted to critical sets in latin squares and the weaker concept of partial latin squares with unique completion. This work involves taking two known partial latin squares with unique completion, or critical sets in latin squares, and using a product construction to produce new partial latin squares with unique completion, or new critical sets in larger latin squares. The results of the fifth chapter are specifically for critical sets of the latin squares which are the direct product of two latin squares, one of which is associated with the cyclic group of order 2 and the other with a cyclic group of odd order. Chapters 3 and 4 of this thesis examine defining sets of some Steiner triple systems (or 2 — (v, 3, 1) designs). The Steiner triple systems studied are those of two infinite families; one is the family of triple systems corresponding to the projective geometries over the Galois field of order 2 and the other is the family of triple systems from the affine geometries over the Galois field of order 3. In each case the geometric structure is used to choose the blocks for the defining sets. A defining set of a design is analogous to a partial latin square with unique completion and a minimal defining set is analogous to a critical set of a latin square. But this is not the only connection between the two topics of this thesis. Results about partial latin squares with unique completion (some of which are new results of my own and some of which were established by others) are used to show that the chosen subsets
Journal Article•
TL;DR: In this paper, a family of critical sets for back circulant latin squares of odd order was identified, where the critical set is the product of the latin square of order 2 with a backcirculant Latin square with odd order, and the proof that each element is an essential part of the reconstruction process relies on the existence of a large number of latin interchanges.
Abstract: To date very Few families of critical sets for latin squares are known. The only previously known method for constructing critical sets involves taking a critical set which is known to satisfy certain strong initial conditions and using a doubling construction. This construction can be applied to the known critical sets in back circulant latin squares of even order. However, the doubling construction cannot be applied to critical sets in back circulant latin squares of odd order. In this paper a family of critical sets is identified for latin squares which are the product of the latin square of order 2 with a back circulant latin square of odd order. The proof that each element of the critical set is an essential part of the reconstruction process relies on the proof of the existence of a large number of latin interchanges.
1 Mar 1996
TL;DR: In this paper, a method for the experimental optimisation of reconfigurable measurement systems able to operate with variable measuring requirements (flexible measurement systems) is proposed, which allows the identification of the configuration characterised by the best performance and is as insensitive as possible to the requirement variations.
Abstract: A method for the experimental optimisation of reconfigurable measurement systems able to operate with variable measuring requirements (flexible measurement systems) is proposed. The proposed method allows the identification of the configuration characterised by the best performance and, at the same time, is as insensitive as possible to the requirement variations. On the basis of the performance typology, a suitable objective function is first selected; then, its maximum at varying configurations is determined by means of a statistical analysis of the results of experiments designed with the aid of orthogonal arrays. In this way, without any loss of result dependability, the experimental effort is reduced with respect to a separate investigation of each configuration. Experimental results of the optimisation of a flexible measurement system operating in a telecommunications company are reported.
TL;DR: In this article, a new construction for orthogonal arrays of strength 3 is given, which is based on the construction of the orthogonality of the beamforming function.
Abstract: A new construction for orthogonal arrays of strength 3 is given.
11 Dec 1996
TL;DR: The purpose of this paper is to identify the optimal factor-level combinations of a simulation model using the backing up of a truck using Taguchi Parameter Design with an L/sub 0/ (3/sup 4/) orthogonal array.
Abstract: How can fuzzy-nets technology perform with greater accuracy and efficiency? The purpose of this paper is to identify the optimal factor-level combinations of a simulation model using the backing up of a truck. Taguchi Parameter Design with an L/sub 0/ (3/sup 4/) orthogonal array was employed to diminish the number of treatment runs.
TL;DR: In this article, a fractional 2m factorial design obtained by assigning factors to fractions of m columns of new saturated two symbol orthogonal arrays which are not isomorphic to the usual ones is proposed.