From the Library of Wow! eBook in .NET Connect datamatrix 2d barcode in .NET From the Library of Wow! eBook

From the Library of Wow! eBook using barcode implement for visual studio .net control to generate, create barcode data matrix image in visual studio .net applications. Oracle's Java Example Problem Interaction Distance E 2 1.0 00 E 1 2.000 X1 5 D: Cup X2 5 E: Ball Actual Factors A: PB = 30.

00 B: Energy = 2.00 C: Stop = 2.00 110 E: Ball 140.

Distance 20 1.00 1.50 2.00 D: Cup 2.50 3.00 Ball-cup interaction plot Distance X1 5 C: Stop X2 5 E: Ball Actual Factors A: PB 5 30.00 B: Energy 5 2.00 D: Cup5 2.00 Distance 74 66 58 50 42. 2.00 3.00 1.75 1.50 E: Ball 2.00 1.25 1.00 1.00 1.50 2.50 C: Stop Distance versus ball and stop From the Library of Wow! eBook 19 . Robustness Optimization Using Taguchi s Methods There are three types of var iables in an OptQuest model: assumptions, decision variables, and forecasts. An assumption variable is described by a probability distribution. While the simulation runs, values for each assumption are sampled from the appropriate distribution.

Decision variables are factors that are varied across a range of values during the simulation. They can be either continuous or discrete. They can also have a random component sampled from the appropriate probability distribution.

The objective of the simulation is to nd settings for the decision variables, derived from the simulation, that satisfy both the objectives and the requirements for the forecasts. In our case, the decision variables are pull-back angle, cup, stop, and energy. The assumption variable is ball type, and the forecast variable is ball throw distance.

A Monte Carlo simulation is run for each set of decision variable settings. The output is a statistical distribution for the forecast variables. In this case the forecast is the throw distance.

Values for the assumption are sampled, the forecast is repeatedly recalculated, and the values are saved. Using the simulation results, the mean and variance of the response are calculated and settings for the decision variable are selected that meet the speci ed criteria for putting the mean on target while minimizing the variance. The important intelligence in the optimization algorithm is how to ef ciently change the decision variables to speed the convergence to settings that will achieve a global rather than local optimum without having to perform an exhaustive search.

In order to prevent convergence on a local optimum, OptQuest uses three different algorithms for sampling the operating space. Table 19.5 shows the acceptable solutions found during the optimization.

The solutions are ranked in order of increasing variance. There is a large difference between the best and worst acceptable solutions, with a worst-case variance of 95.3 and best case of 10.

6. In OptQuest, a requirement must be satis ed. Our requirement is a mean throwing distance of 72 inches when using both the plastic ball and the golf ball.

An objective is the best that can be achieved for a given performance metric while meeting the requirement. Our objective is to minimize the variance. Figures 19.

11 and 19.12 show the results of the simulation using the best and worst acceptable settings. There are two contributors to the variability observed in the simulation: the ball and the residuals.

Figure 19.11 shows the best-case settings that minimize the difference between the plastic and golf balls. In Figure 19.

12, which is the worst case from the simulation, we can see the separate contributions of the ball and the residuals. The difference in the masses of the plastic ball and the golf ball moves the individual distributions for each ball farther apart. The individual distributions are caused by the residuals.

The distribution of higher values is for the plastic ball, while the one of lower values is for the heavier golf ball. If we look at the difference in robustness, comparing best case to worst case, the difference in terms of S/N is given by (S>N) = 10 log a s2 w s2 B b = 10 log a 95.3 b 10.

6. (19.9). This is a difference of 9.5 dB, which translates to a reduction in quality loss of nearly 89%! Conclusions Comparing Orthogonal Array Results to RSM In the catapult example, we see that the orthogonal array got us to the same set of control factor settings as did the response surface experiment and stochastic optimization. Even though there were signi cant control factor interactions, they were not large enough to lead us to wrong.

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