Abstract: A new nonlinear skewing scheme is proposed for parallel array access. We introduce a new Latin square(perfect Latin square) which has several properties useful for parallel array access. A sufficient condition for the existence of perfect Latin squares and a simple construction method for perfect Latin squares are presented. The resulting skewing scheme provides conflict free access to various subsets of an N x N array using N memory modules. When the number of memory modules is an even power of two, address generation is performed in constant time using a simple circuit. This scheme is the first memory scheme that achieves constant time access to rows, columns, diagonals, and N1/2 x N1/2 subarrays of an N x N array using the minimum number of memory modules.

Abstract: [This abstract is based on the author's abstract.] Great caution must be used when applying the three-level Latin square (L9 orthogonal array) experimental design for more than two factors. Statistical two-factor interactions seriously bias the ave..

Abstract: Robust design is an efficient method for designing high quality products at low cost. The method examines the effect of a large number of design factors on the variability of a product's response due to various sources of disturbance. This effect can be observed efficiently by studying a large number of variables simultaneously through balanced, orthogonal array experiments, and by analyzing the resulting data using variance decomposition methods. In this paper we describe an expert system prototype for designing efficient experiments. Given the information on various parameters and their levels, the system designs an experiment using orthogonal arrays. This expert system is implemented in Prolog, which is a logic programming language for artificial intelligence research and expert systems development. The system was implemented under the P-Shell knowledge programming environment on UNIX.

Abstract: In the last several years, the use of designed experiments in manufacturing and engineering design environments has become increasingly popular through the introduction of the ideas of Dr. G. Taguchi. The Taguchi Method, a systematic technique for experimental design and analysis, employs team oriented solutions to analyze design and production problems and their causes. The Taguchi Method as provided a simplified approach to the design of statistically significant experiments. This has greatly increased the number of experimental design practitioners. This paper presents a computer program that addresses the need for an automated system able to design the experimental matrices for the orthogonal arrays that are required by Taguchi's Method. The program was written tode sign simple arrays as well as complex multi-level arrays with two-way interactions.

Abstract: An important reason behind the success of the Taguchi methodology in qual- ity assurance has been the use of statistical methods, presented in a way that is accessible to the nonexpert user. Among the tools used to simplify the sta- tistical design of experiments has been the linear graph, apparently introduced by Taguchi. However, he did not consider the resolution of the corresponding designs (the higher the resolution, the more accurate the conclusions). For example, it will be shown that half of the linear graphs given by Taguchi for the L16(215) orthogonal array correspond to designs of resolution III, when designs of resolution IV are available (with the same lines in the linear graphs but with different assignments to the columns of the orthogonal array). A nontraditional but very straightforward method is presented for obtaining the alias chains and the linear graphs corresponding to an orthogonal array. The procedure can be easily understood and employed by nonstatisticians to find an experimenta...

Abstract: The Taguchi Method is an empirical way of improving the quality of a product or process (a system) It consists of experimentally determining the levels of the system’s parameters so that the system is insensitive (robust) to factors that make it’s performance degrade, Phadke & Dehnad[1] The successful application of this method to various engineering problems has generated an interest among statisticians in studying the methodology and casting it in a traditional statistical framework A concept of particular interest has been the notion of “Signal to Noise Ratio” (S/N ratio) that Professor Taguchi uses to measure the contribution of a system parameter1 to variability of the functional characteristics of that system Moreover, he uses the S/N ratio in a two step optimization procedure that aims at reducing the variability of these functional characteristics by the proper setting of these parameters The first step consists of conducting highly fractional factorial experiments (Orthogonal Array Designs) at various levels of the system’s parameters and using the data to select those levels that maximize the S/N ratio This reduces the variability of the functional characteristic of the system However, this characteristic might have some deviation from its desired value and the next step is to eliminate such deviations through proper adjustment of a system’s parameter called the “adjustment factor”2

Abstract: : It is shown that Bush's bound for maximum number of constraints in an orthogonal array of index unity is uniformly better than Rao's bound. In addition it is shown, using an argument similar to that needed in the proof of the above result, that Noda's characterization of parameters in orthogonal arrays of strength 4 achieving equality in Rao's bound, leads easily to a similar characterization in arrays of strength 5. These results are useful designing experiments for quality control.

Abstract: An algorithm for designing orthogonal digital filters using a purely state-space approach is developed. The algorithm consists of three parts: (i) orthogonal embedding, (ii) transformation of the embedded orthogonal transition matrix to the extended upper Hessenberg form, and (iii) factorization of this new form into into (2n+1) Givens rotations. Appropriately interconnecting the rotors leads to the pipelined orthogonal filter structure. As a consequence of this approach, an essentially orthogonal structure is obtained for the inverse filter, and only one Givens rotor gets replaced by a hyperbolic rotor. >

Abstract: The work described in this paper has been motivated by two different, but related, problems that arise in the analysis of computer performance. The first is how to set an operating system’s tunable parameters1 to achieve the best response time for interactive tasks, given the computer’s load conditions. The second is how to map the relationship among the different tunable parameters of the system and their impact on response time.

Abstract: An important problem in studying orthogonal arrays is the determination of the maximum number of factors that can be accommodated in such an array. A slightly easier and more tractable problem is to determine the maximum number of factors that can be accommodated in an orthogonal array if consideration is restricted to arrays that can be constructed through a particular method. This paper describes two such methods of construction and shows that the maximum numbers of factors under these two methods are the same.

Abstract: A method of constructing a resolvable orthogonal array (4λk2,2) which can be partitioned into λ orthogonal arrays (4,k 2,1) is proposed. The number of constraints kfor this type of orthogonal array is at most 3λ. When λ=2 or a multiple of 4, an orthogonal array with the maximum number of constraints of 3λ can be constructed. When λ=4n+2(n≧1) an orthogonal array with 2λ+2 constraints can be constructed. When λ is an odd number, orthogonal arrays can be constructed for λ=3,5,7, and 9 with k=4,8,12, and 13 respectively.