Experimentation for Engineers by David Sweet

Author:David Sweet [Sweet, David]
Language: eng
Format: epub
Published: 2023-01-26T23:00:00+00:00

Figure 4.14 Design for a two-parameter (2D) experiment. (a) You need a minimum of three threshold values, (0.5, 1.0, and 1.5) to be able to interpolate the maximum markout_profit_2D(threshold, order_size) at a threshold between the left and right edges, threshold = 0.5 and threshold = 1.5. (b) Similarly, you’ll measure three values of order_size (1, 1.5, and 2) to ensure that we can interpolate between the top and bottom edges. (c) In a single experiment, you can measure these five values simultaneously. When you analyze the experiment, you’ll be able to interpolate markout_profit_2D(threshold, order_size) from the edges to center.

Figure 4.14(c) shows a design to measure five combinations of the parameters (threshold, order_size): (0.5, 1.5), (1.0, 1.5), (1.5, 1.5), (1.0, 1.0), and (1.0, 2). With measurements of markout_profit_2D(threshold, order_size) and each of those points, you’ll be able to interpolate well near any of the four edges and near the center and use that interpolation to seek the optimize parameter combination (threshold_opt, order_size_opt).

You’re not done yet, though. There’s more space in the square in figure 4.14(c) to interpolate over than the edges and the middle. Since the optimum could be anywhere in this box, it’s possible that the optimum you seek is in a corner. To be sure the interpolation is accurate near the corners, you should pay the extra experimentation cost and add four points in the corners of the design. The result is a face-centered central composite design (CCD), depicted in figure 4.15.

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