Welch, W.J., Yu, T.K., Kang, S.M. and Wu, J., 1990, "Computer Experiments for Quality Control by Parameter Design," Quality Technology, Vol. 22, pp. 15-22.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Tsui, 1992, argues that many of Taguchi s statistical methods, e.g. orthogonal arrays, linear graphs and accumulation analysis, are not statistically efficient. Box, 1988, points out that there are various mathematical difficulties requirements associated with the use of signal tonoise ratio. Welch, et al. 1990, propose combining control and noise factors into a single array thus modeling the response rather than expected loss, and approximating a prediction model for loss based on the fitted response model. This response model approach is further developed by Shoemaker, et al. 1991. These proposed ....

....control and noise factors using the Response Surface Methodology (RSM) Step 2. Derive functions of mean and variance of the responses based on the type of robust design applications. Step 3. Use the compromise DSP to find the robust design solution. In Step 1, the response model approach (Welch, et al. 1990: Shoemaker, et al. 1991) is applied to overcome the limitations of Taguchi s loss model approach. Using an integrated design analysis program as the simulation module, instead of applying Taguchi s inner and outer array approach, control and noise factors are put in a single array for computer ....

Welch, W.J., Yu, T.K., Kang, S.M. and Wu, J., 1990, "Computer Experiments for Quality Control by Parameter Design," Quality Technology, Vol. 22, pp. 15-22.

....are outlined. An important advantage in the optimization stage is that uncertainty in the parameter estimates is accounted for in the model. For robust design experiments, the Bayesian approach easily incorporates the variability of the noise factors using the response modeling approach (Welch, Yu, Kang and Sacks 1990 and Shoemaker, Tsui and Wu 1991) This approach and its techniques are used to analyze two data sets, one which arises from a robust design experiment. Key Words: Binary Data, Generalized Linear Model, Gibbs Sampler, Robust Design. 1 1 Introduction Data sets with an ordered categorical ....

....are set at xed levels, however. First, the response is modeled as a function of both the control and noise factors. Then the noise factors are assumed to follow a speci c distribution. This allows control settings that desensitize the response to the variation in the noise factors to be chosen (Welch, Yu, Kang and Sacks 1990 and Shoemaker, Tsui and Wu 1991) Note that for the Bayesian model, the distribution of p now has two di erent components the posterior for ( and the distribution of the noise factors. The calculation of the distribution of proportions is simple, and the additional distributions introduced ....

Welch, W. J., Yu, T. K., Kang, S. M. and Sacks, J. (1990), \Computer Experiments for Quality Control by Parameter Design," Journal of Quality Technology, 22, 15-22.

....variation in O transmitted to the response. In this article, the error terms are assumed to be i.i.d. If the replicates were not randomized (as is probably the case) a hierarchical model could be used. Two classes of methods for the analysis of robust design data are the response model approach (Welch et al. 1990) and the summary measure approach. The former models the response directly and treats the noise variables as fixed for the purpose of model building (I) In (II) regular production conditions are simulated by assuming a distribution for the noise variables, which induces extra variation in Y . By ....

Welch, W. J., Yu, T. K., Kang, S. M. and Sacks, J. (1990). "Computer Experiments for Quality Control by Parameter Design," Journal of Quality Technology, 22, 15--22.

....order polynomials to analyze computer experiments. The cyclone study was originally a case study in robust design. We choose this study to demonstrate the link between computer experiments and robust designs. Robust design studies can also be carried out using computer models as presented by Welch et al. 1990). Orthogonal Latin Hypercube design and Symmetric Latin Hypercube design can be used in a robust design 24 study as well. One can follow the response model approach of robust designs as proposed in Welch et al. 1990) and Shoemaker, Tsui and Wu (1991) First, establish a prediction model for both ....

....design studies can also be carried out using computer models as presented by Welch et al. 1990) Orthogonal Latin Hypercube design and Symmetric Latin Hypercube design can be used in a robust design 24 study as well. One can follow the response model approach of robust designs as proposed in Welch et al. 1990) and Shoemaker, Tsui and Wu (1991) First, establish a prediction model for both control and noise factors. Then, given the distribution of noise variables, estimate the variation of Y for each combination of control variables using the model obtained at the first stage. If a computer experiment ....

Welch, W. J., Yu, T. K., Kang, S. M. and Sacks, J. (1990). Computer experiments for quality control by parameter design. Journal of Quality Technology, 22, 15-22.

....allows one to consider f to be deterministic, and in particular to avoid having to specify a distribution for f . The material given there expands on a proposal of Owen [49] There is still much more to be done. 4 Bayesian prediction and inference A Bayesian approach to modeling simulator output [68, 69, 87] can be based on a spatial model adapted from the geo statistical Kriging model [36, 29, 12, 62] This approach treats the bias, or systematic departure of the response surface from a linear model, as the realization of a stationary random function. This model has exact predictions at the observed ....

....p Y j=1 R j (jx 1j Gamma x 2j j) is often used for mathematical convenience. That is, R( Delta) is a product of univariate correlation functions and hence, only univariate correlation functions are of interest. The product correlation function has been used for prediction in spatial settings [89, 13, 69, 68, 87]. Several choices for the factors in the product correlation function are outlined below. 4.3.2 Cubic The (univariate) cubic correlation family is parameterized by ae 2 [0; 1] and fl 2 [0; 1] and is given for d 2 [0; 1] by R(d) 1 Gamma 3(1 Gamma ae) 2 fl d 2 (1 Gamma ae) 1 Gamma ....

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Welch, W. Yu, T., Kang, and Sacks, J. Computer experiments for quality control by parameter design. Journal of Quality Technology, 22:15--22, 1990.

....necessity of one shot experiments disappears. 4 Another Approach to Robust Design In contrast to Taguchi s emphasis on modeling SNRs, various researchers have advocated directly modeling the response as a function of both control and noise factors. The approach that we describe was proposed by Welch, Yu, Kang and Sacks (1990). Suppose that we measure q quality characteristics, y 1 ; y q . Let y i (x; denote the value of the ith quality characteristic when the control and noise factors assume values (x; and let l[y 1 (x; y q (x; denote the loss that accrues from the qualities attained at ....

....control and noise factors will usually require far fewer observations than Taguchi s crossed arrays, even when interactions between the control factors are included. Second, the y i (x j ; j ) are used to construct cheap to compute surrogate models y i . These may be regression models, as in Welch, Yu, Kang, and Sacks (1990), or spatial statistical models for computer experiments, as in Welch and Sacks (1991) Third, optimization is carried out using the surrogate objective function L(x) Z l[y 1 (x; y q (x; w( d : Thus, just as with Taguchi s methods, one relies on a one shot experiment: all ....

Welch, W. J., Yu, T. K., Kang, S. M., and Sacks, J. (1990). Computer experiments for quality control by parameter design. Journal of Quality Technology, 22:15--22.

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W. J. Welch, T.-K. Yu, S. M. Kang, and J. Sacks, "Computer Experiments for Quality Control by Parameter Design," J. Quality Technol., 22, pp. 15-22 (1990).

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Welch, W. J., Yu, T.-K., Kang, S. M. and Sacks, J., "Computer Experiments for Quality Control by Parameter Design," Journal of Quality Technology, Vol. 22, No. 1, 1990, pp. 15-22.

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Welch, W.J., Yu, T-K, Kang, S.M. and Sacks, J. (1991) Computer experiments for quality control by parameter design, Journal of Quality Technology 22, 15-- 22.

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