Abstract: Robust Design is an important method for improving product quality, manufacturability, and reliability at low cost. Taguchi's introduction of this method in 1980 to several major American industries resulted in significant quality improvement in product and manufacturing process design. While the robust design objective of making product performance insensitive to hard-to-control noise was recognized to be very important, many of the statistical methods proposed by Taguchi, such as the use of signal-to-noise ratios, orthogonal arrays, linear graphs, and accumulation analysis, have room for improvement. To popularize me use of robust design among engineers, it is essential to develop more effective, statistically efficient, and user-friendly tech niques and tools. This paper first summarizes the statistical methods for planning and analyzing robust design experiments originally proposed by Taguchi; then reviews newly developed statistical methods and identifies areas and problems where more resear...

Abstract: A method and apparatus is provided for estimating signal power. The estimating is accomplished by correlating (206) an input data vector (204) with a set of mutually orthogonal codes to generate a set of output values. The input data vector (204) consists of data samples of a received orthogonal coded signal (202). Each output value corresponds to a mesure of confidence that the input data vector is substantially similar to one of the orthogonal codes from within the set of mutually orthogonal codes. Finally, an estimate of the power of the received orthogonal coded signal is generated (208) as a nonlinear function of the set of output values.

Abstract: This paper presents a methodology to incorporate manufacturing and operational variances in the design optimization stage to achieve robust and optimal performance. The procedure uses Taguchi's orthogonal arrays to approximate the expected value of performance during optimization. This approach reduces the number of function evaluations in problems that use computationally expensive performance simulation programs. The method allows incorporation of variances on many variables simultaneously. This paper uses two illustrative examples: (1) Design of helical gears that have minimum transmission error and at the same time are less sensitive to manufacturing errors, (2) Design of beverage cans where we minimize the effects of errors in tooling on can weight and structural requirements. The optimal robust design shows a considerable decrease in sensitivity to manufacluring and operational variances and, at the same time, has good performance.

Abstract: General techniques for the construction of asymmetrical orthogonal arrays of strength 2 are presented. These are then applied to special cases to obtain new families of such arrays. Among these are saturated main-effect plans based on $s^m$ runs with factors at $s^{ u_i}$ levels, $i = 0, 1, \ldots, r,$ where $m \geq v_r, v_0 = 1, v_{i-1}$ divides $v_i, i = 1,2,\ldots, r$, and $s$ is a prime power.

Abstract: The theory of (t, m, s)-nets is useful in the study of sets of points in the unit cube with small discrepancy. It is known that the existence of a (0, 2,s)-net in baseb is equivalent to the existence ofs−2 mutually orthogonal latin squares of orderb. In this paper we generalize this equivalence by showing that fort≥0 the existence of a (t, t+2,s)-net in baseb is equivalent to the existence ofs mutually orthogonal hypercubes of dimensiont+2 and orderb. Using the theory of hypercubes we obtain upper bounds ons for the existence of such nets. Forb a prime power these bounds are best possible. We also state several open problems.

Abstract: A diagonal Latin square is a Latin square whose main diagonal and back diagonal are both transversals. In this paper we give some constructions of pairwise orthogonal diagonal Latin squares. As an application of such constructions we obtain some new infinite classes of pairwise orthogonal diagonal Latin squares which are useful in the study of pairwise orthogonal diagonal Latin squares.

Abstract: The primary aim of this paper is to demonstrate how the ‘design-of-experiments’ techniques which are successful in physical experiments could also be adapted to a numerical simulation code. As an example this technique is applied to a general finite difference code used for predicting three-dimensional turbulent recirculating flows. Here the equations for velocities and continuity are solved using the algorithm called SIMPLE, which stands for semi-implicit method for pressure-linked equations. Physical modelling of turbulence is taken care of by means of kinetic energy and turbulence dissipation rate equations. The objective is to optimize the underrelaxation factors of primary and secondary flow variables so that the number of iterations required for convergence is minimum. This is done by the orthogonal array technique (a particular type of design-of-experiment technique). The geometry considered for this purpose is that of a simple gas turbine can combustor and the study is restricted to the isothermal non-reacting condition. Tests are carried out on three different grid configurations. In each case the underrelaxation factor for velocities contributed most to speed up the rate of convergence. Also, for each grid configuration the underrelaxation factor settings for minimum iterations for convergence was found to be same. Hence it is proposed that when doing grid independence tests for any similar flow situation, all the underrelaxation factors could be optimized on coarse grids.

Abstract: : The use of mixed multilevel orthogonal arrays in robust design has gained popularity in quality improvement areas in recent years. We have investigated the use of genetic algorithms in the construction of such arrays. This paper addresses issues encountered in formulating the problem (such as encoding and representation), as well as the results of this application. We compare this technique with simulated annealing which we published previously.

Abstract: We use the simulated annealing algorithm to construct mixed multilevel balanced orthogonal arrays. We demonstrate how this algorithm can be used to find the multilevel balanced experimental design matrix with the minimal number of runs. These orthogonal arrays are widely used in the quality improvement projects. By formulating the problem as an optimization problem, we show that simulated annealing can find the global optimum, while avoiding being trapped in local extrema. An important application of our results is in experimental designs where variables are discrete in nature. A well balanced design not only saves experimental cost but also arrives at conclusions robust to environmental changes.

Abstract: Hierarchical redundancy using defect-tolerant replacement circuits is proposed for increasing the yield of large-area LSIs (WSIs) with mesh-connected array structures. The defect-tolerant replacement circuits can be constructed by using direct-connection paths and distributed switches in basic k-out-of-n redundancy schemes. When the proposed redundancy configurations are applied to two-dimensional orthogonal-array WSIs (wafer-scale-integrated circuits), they reduce the number of switches not covered by any spare replacements. An estimate of defect tolerance indicates that the proposed redundancy configurations can increase the integration scale under 1-micron CMOS design about 256 times over that of general nonredundant LSIs. >

Abstract: The neural network and orthogonal array are introduced for statistical circuit design. As an alternative to quadratic approximation, a back-propagation neural network is utilized as a classifier and employed to nonlinearly approximate to the feasible region in the circuit element space to improve the accuracy of approximation. The orthogonal array, which has found wide applications in experimental design, is exploited for design centering and speeding up the yield optimization process. An 11-element low-pass filter is given as a design example to show that the efficiency of the new method is higher than that of the quadratic approximation method. >

Abstract: Based on the principle of the orthogonal method for large-scale experiment design, an efficient rotating orthogonal method is developed to search for the near-optimal solution of combinatorial optimization. Since many problems of integer programming can be converted into zero-one integer programming, a novel efficient method for generating the large-scale 0-1 orthogonal table is proposed. The search algorithm does not find the optimal solution in a purely random way, but searches along an orthogonal table, rotating the table in sequence according to the order of extreme differences of variables, i.e., according to the importance of variables. The concept and basic principles, the construction of 0-1 orthogonal tables, and the search algorithm and its effectiveness are examined using examples. >

Abstract: To control product quality without expensive control methods, Robust Design (Taguchi method) was used to classify control and signal factors from all parameters in an aluminum coloring process. By using orthogonal arrays and S/N analysis, control factors for film thickness, including coloring concentration (A), current density (E), and desmutting time (G), have been successfully determined. Meanwhile, a signal factor, anodizing time (D), has also been identified

Abstract: The authors present an improved approach to one-step C-testability of orthogonal two-dimensional iterative logic arrays. This is an improvement of the approach of W. Huang and F. Lombardi (1988) and H. Elhuni et al. (1986). A group of sufficient conditions to test two-dimensional iterative logic arrays with a constant number of test vectors independent of the array size (C-testability) is stated. It is proved that the proposed approach requires a smaller number of test vectors than in previous works. >

Abstract: A new method of construction of orthogonal resolution IV designs for symmetrical and asymmetrical factorials has been presented. Many new series of orthogonal factorial designs of resolution IV can be obtained by the above general method.

Abstract: In running a factorial experiment, it may be desirable to use an orthogonal array with different (mixed) numbers of factor levels. Because of the orthogonality requirement, such arrays may have a large run size. By slightly sacrificing the orthogonality requirement, we can obtain nearly orthogonal arrays with economic run size. Some general methods for constructing such arrays are given. For 12, 18, 20, and 24 runs, many orthogonal arrays and nearly orthogonal arrays with mixed levels are constructed and tabulated. Effects of near orthogonality on estimation efficiency and analysis are studied.