R. Myers and D. Montgomery. Response Surface Methodology: Process and Product Optimization Using Designed Experiments. Wiley, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....individual product performance within a product family described by a range of performance requirements. 4. 2 Verification Based on Model Behavior To gain a better understanding of the physical behavior of the example problem, response surface models were developed (see, e.g. Myers and Montgomery [16]) of the different motor performance using the OPTIMUS software. The response surface models are developed for the torque (T) power (P) efficiency (Z) and mass (M) of each motor in the neighborhood of the optimum solution obtained by the VBPDM (see Table I) Each response surface is ....

Myers, R. H. and Montgomery, D. C. (1995). Response Surface Methodology: Process and Product Optimization Using Designed Experiments. John Wiley and Sons, New York.

....and each may only be available for a single experiment. The nal result will not be a single additional selection from the set, but a selection of many candidates from a set of untested possibilities. 1.1 Related Work Design of experiments is an important topic in the statistics literature. See [10] for an overview. DOE is primarily concerned with continuous valued input variables. Most of these methods have relatively straightforward extensions to discrete input variables, but do not scale to the cases of large numbers of discrete input variables and large arity discrete variables. Active ....

R. Myers and D. Montgomery. Response Surface Methodology: Process and Product Optimization Using Designed Experiments. Wiley, 1995.

.... of a Two input Response Surface With regard to design of a complex engineering system, the response surface methodology (RSM) allows the design space to be efficiently explored to determine the values of the design variables that optimize performance characteristics subject to system constraints [12]. RSM is used to obtain the mathematical models that approximate the functional relationships between performance characteristics and design variables [13] Various design of experiments techniques, such as the central composite design (CCD) and the Box Behnken design, are used to sample the ....

....of Empirical Models 4.1.1.Linear Regression In most applications of RSM, it is necessary to develop an approximation model to the true response surface. Approximation is necessary since, for most cases, the underlying function that drives the response is an unknown physical mechanism [12]. Multiple regression is used to generate an empirical model. A multiple linear regression model with n independent variables takes the form ## # # # where y represents the response value, x i are the independent variables (predictor variables or regressors) # i are unknown partial ....

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Myers, R. H. and Montgomery, D.C.: Response Surface Methodology: Process and Product Optimization Using Designed Experiments, New York: Wiley, 1995.

....parameter in turn. Scatter plots with a uniformly distributed cloud of points indicate parameters with little influence on the results, whereas scatter plots with a defined shape to the cloud indicate parameters which are more significant. Related techniques include analysis of variance (ANOVA) [51] and primary effects analysis, in which the parameters which have the greatest influence on the results are identified from sampling results. 9.2 LHS The Latin hypercube sampling method was developed by McKay, et al. 46] as an alternative to random sampling. Under certain monotonicity conditions ....

....using quadratic polynomials. The quadratic polynomial surface fit may not be the best choice for modeling data trends over the entire parameter space, unless the trend is close to quadratic. Quadratic polynomials can be inaccurate if used to model data trends that are cubic or higher order. See [51] for more information on quadratic models. 14.4 First order Taylor Series Models The first order Taylor Series model is purely a local approximation method. That is, it provides local trends in the vicinity of a single point in parameter space. The form of the Taylor Series model is (15) where x ....

Myers, R. H., and Montgomery, D. C., Response Surface Methodology: Process and Product Optimization Using Designed Experiments, John Wiley & Sons, Inc., New York, NY, 1995.

....when a higherorder (quadratic or cubic) polynomial model is necessary to accurately predict a response or when the experimenter simply wants more detail of the response behavior in a specific region. That increased detail facilitates the optimization and system tuning desired by the experimenter [13]. The next two sections present the construction of the two most popular response surface designs: the central composite and the Box Behnken designs. 2.5.1 Central composite After a two level factorial design has been completed, the resulting empirical model may not predict the observed response ....

....2.8 represent the four 2 factorial experiments. Each of the four axial points is at distance from the center point at the origin. The axial and center points provide additional information to the factorial data, so that a quadratic or higher degree polynomial model can be fit to the response [13]. The fact that each CCD contains a two level factorial design makes the CCD wellsuited for sequential experimentation. Often, the factorial experiments are already complete before the CCD is created. Early factorial experiments may produce a model that does not fit the observed response. Only 2k ....

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R. H. Myers and D. C. Montgomery, Response Surface Methodology: Process and Product Optimization Using Designed Experiments. New York, New York: John Wiley & Sons, 1995.

....both are widely used in industry, the response surface approach is often advocated because of its stricter reliance on well established techniques for statistical modeling, analysis, and experimental design. Consider the following response surface model widely used in robust design studies [9]. The output response y is represented as y = at (x) w w Bx (1) where x= xl, x2 . Xp] is a vector ofp controllable input variables, w = Wl, w2 . win] is a vector of m uncontrollable noise variables, and, is the model residual error. It is assumed that w is random with mean zero ....

....the x settings, with the objective of developing a robust design method that is itself robust to model estimation errors. In spite of the large amount of research in the area of robust design, there has been relatively little work on how to consider model uncertainty. Notable exceptions are [9] and [10] 9] focuses primarily on model parameter uncertainty and discusses a graphical approach in which the mean and variance responses are plotted as functions of x, while simultaneously displaying a confidence region for the x settings that truly minimize Vare, w(y ) These truly optimal x ....

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Meyer, R. H. and Montgomery, D., 1995, Response Surface Methodology: Process and Product Optimization Using Designed Experiments. John Wiley & Sons, New York, N.Y.

....mold filling time. 1) 2) There have been many creative methods discussed in the statistics literature for treating multiple response problems. The performances of these techniques are dependent on or limited by the size and complexity of the problem. Approaches include graphical techniques [2], linear programming [3] multiobjective algorithms that produce a Pareto optimal set of solutions [4, 5] and desirability functions [6 9] The desirability function approach is commonly used because of its ease of i mplementation. Desirability functions are utility functions that convert ....

Myers, R. H., and Montgomery, D. C., 1995. Response Surface Methodology: Process and Product Optimization Using Designed Experiments, John Wiley & Sons, Inc. New York, NY.

....(philosophically similar to fixed scan schedules) but the schedulers are still dynamic and hence information obtained during the mission can be exploited to enhance performance. One approach to solve an optimization problem as general as this is to use a tesponse surface method ology (RSM) [8] where Monte Carlo simulations are used to characterize the performance of a DSS with a particular set of parameters for range of possible emitter environments. A plot of the performance measure vs. DSS parameters provides a tesp onse surface that characterizes how well the DSS will perform over ....

R.H. Meyers and D.C. Montgomery, editors. Response Surface Methodology: Process and Product in Optimization Using Designed Experiments. John Wiley and Sons, Pub., New York, NY, 1995.

....12 15) The values of the 7 configuration factors (Table 3) The values of the configuration deviation variables d i , d i (i = 5 9; corresponding to goals, Eqns. 19 23) Satisfy: SFC 1.030 lbm h lbf normalized [8] Thrust 990 lbf normalized [9] Mixing pressure ratio (Phot Pcold) 0. 94 [10] SFC 0.96 d 1 = 1 [12] STDSFC 0.01 d 2 = 1 [13] THRUST 1052 d 3 = 1 [14] STDTHR 29 d 4 = 1 [15] Weight 1425 lbs [16] Length 7 ft [17] Fan diameter 38.4 in [18] Thegoals: WEIGHT 1350 d 5 = 1 [19] STDWGT 0.005 d 6 = 1 [20] LENGTH 6 d 7 = 1 [21] STDLNG 0.02 ....

Myers, R.H. and Montgomery, D.C., Response Surface Methodology: Process and Product Optimization using Designed Experiments, Wiley Series in Probability and Statistics, New York, John Wiley & Sons, 1995.

....approach We have developed a sequential approximate optimization strategy based on linear response surface approximations of objective function and constraints. Each linear approximate subproblem is built from N experiments that are planned according to a D optimal experimental design [3] within the search subregion under consideration. This approximate subproblem is then solved by a branch and bound integer linear programming solver. The calculated approximate design is evaluated on the basis of M replications of the simulation experiment. If the design is accepted, the design ....

Myers, R.H.; Montgomery, D.C. 1995: Response Surface Methodology - process and product optimization using designed experiments. New York: John Wiley & Sons.

....issues, have led researchers to try to reduce the number of variables that need to be considered, both in terms of inputs and outputs from a simulation code. The use of metamodels or response surfaces represents this approach, which is often useful in dealing with complex modeling situations [7, 8]. However, as we will discuss below, it may be useful in some situations to think about uncertainties in the broader context of the full simulation. We have ignored the potential uncertainties in the experimental set up. These are readily included in the Monte Carlo technique. For example, to ....

R. H. Myers and D. C. Montgomery, Response Surface Methodology: Process and Product Optimization Using Designed Experiments (Wiley Inter-science, New York, 1995)

....is a good rule of thumb to overfit polynomial models whenever possible. 6.2.3 Surrogate Model Construction The version of DAKOTA used in this study employed four surrogate modeling techniques. These were: 1) kriging spatial interpolation [20, 21] 2) quadratic polynomial regression (QuadPoly) [22]; 3) multivariate adaptive regression splines (MARS) 23] and (4) stochastic layered perceptron artificial neural networks (ANN) 24] The kriging, MARS, and ANN methods do not assume a particular trend in the data. That is, these three surrogate modeling methods can capture arbitrary ....

Myers R. H., and Montgomery, D. C., Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Wiley, New York, 1995, pp. 79-123.

.... when noise dominates the differences between simulation output between vertices, is more efficient than the basic algorithm [6] Other approaches that consider the model to be a black box that does not give information on gradients or higher order derivatives are the Response Surface methodology [7], 8] and the Stochastic Approximation method [9] These methods use evaluations of the objective function of a simulation model for different parameter values to calculate estimates of derivatives that are then used in optimization routines. Opening the black box to obtain information during the ....

R.H. Myers and D.C. Montgomery, Response surface methodology: process and product optimization using designed experiments , New York: John Wiley & Sons, 1995

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R. Myers and D. Montgomery. Response Surface Methodology: Process and Product Optimization Using Designed Experiments. Wiley, 1995.

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R.H. Myers and D.C. Montgomery. Response Surface Methodology: Process and Product Optimization Using Designed Experiments. J. Wiley & Sons, New York, 1995.

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Myers, R.H., Montgomery, D.C., 1995. Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Wiley Inter-science, New York, NY.

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Myers, R.H., Montgomery, D.C., Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Wiley Inter-science, New York, 1995.

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R.H. Myers and D.C. Montgomery. Response Surface Methodology: Process and Product Optimization Using Designed Experiments. John Wiley & Sons Inc., 1995.

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Myers, R. H. and Montgomery, D. C., 1995, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, John Wiley & Sons, New Yo r k

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Myers, R. H., and Montgomery, D. C., Response Surface Methodology: Process and Product Optimization Using Designed Experiments, New York: John Wiley & Sons, Inc. 1995.

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) Myers, R. H., and D. C. Montgomery, "Response Surface Methodology, Process and Product Optimization Using Designed Experiments," New York, John Wiley and Sons, 1995.

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Myers, R.H., Montgomery, D.C., Response Surface Methodology: Process and Product Optimization Using Designed Experiments, John Wiley & Sons Inc., 1995

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Myers, R.H., Montgomery, D.C., Response Surface Methodology: Process and Product Optimization Using Designed Experiments, John Wiley & Sons, Inc., 1995.

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Myers RH, and Montgomery DC. Response Surface Methodology: Process and Product in Optimization Using Designed Experiments. New York: Wiley, 1995.

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Myers, R.H. and Montgomery, D.C., Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Wiley, New York, NY, 1995.

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