Space experiment

The location of a point on the response surface must be specified by (1) stating the level of the factor, and (2) stating the level of the response. Stating only the coordinate of the point with respect to the factor locates the point in factor space stating only the coordinate of the point with respect to the response locates the point in response space and stating both coordinates locates the point in experiment space. If the seventh experimental observation gave the third point from the left in Figure 2.3, the location of this point in experiment space would by x,7 = 3.00, y = 4.76 (the first subscript on x and y refers to the factor or response number the second subscript refers to the experiment number). 

Sketch the factor space, response space, and experiment space for Problem 2.1. 

In Chapter 2 it was seen that a response surface for a one-factor system can be represented by a line, either straight or curved, existing in the plane of two-dimensional experiment space (one factor dimension and one response dimension). In two-factor systems, a response surface can be represented by a true surface, either flat or curved, existing in the volume of three-dimensional experiment space (two factor dimensions and one response dimension). By extension, a response surface associated with three- or higher-dimensional factor space can be thought of as a hypersurface existing in the hypervolume of four- or higher-dimensional experiment space. 

Figure 12.3 is a pseudo-three-dimensional representation of a portion of the three-dimensional experiment space associated with the system shown in Figure 12.1. The two-dimensional factor subspace is shaded with a one-unit grid. The factor domains are again 0 < Xj < +10 and 0 < < +10. The response axis ranges from 0...

Figure 12.3 Location of a single experiment in three-dimensional experiment space.

In general, if k is the number of factors being investigated, the full second-order polynomial model contains V2 k -t- 1)(A -h 2) parameters. A rationalization for the widespread use of full second-order polynomial models is that they represent a truncated Taylor series expansion of any continuous function, and such models would therefore be expected to provide a reasonably good approximation of the true response surface over a local region of experiment space. 

Experiences Space for comments on case specific experiences... 

Space shuttle -microgravity experiments [SPACE PROCESSING] (Vol 22) -use of ablative materials [ABLATIVE MATERIALS] (Vol 1) -use of high temperature alloys [HIGH TEMPERATURE ALLOYS] (Vol 13)... 

Figure 2.3, the location of this point in experiment space would be x17 = 3.00, ytl = 4.76 (the first subscript on x and y refers to the factor or response number the second subscript refers to the experiment number). 

Figure 11.3 is a pseudo-three-dimensional representation of a portion of the three-dimensional experiment space associated with the system shown in Figure 11.1. The two-dimensional factor subspace is shaded with a one-unit grid. The factor domains are again 0 < xl < +10 and 0 < x2 < +10. The response axis ranges from 0 to +8. The location in factor space of the single experiment at xn = +3, x2l = +7 is shown as a point in the plane of factor space. The response (yn = + 4.00) associated with this experiment is shown as a point above the plane of factor space, and is connected to the factor space by a dotted vertical line.

Spacing of wicks in the field is often in the range of 4 to 8 feet. Contractors may have a feel for proper spacing based on their own experience. Spacing may also be determined by using the design procedure in the previous example, and selecting 6-inch-diameter sand drains, with the intent to use wicks. Suppose, in the previous example, 6-inch sand drains... 

Figure 13.42 illustrates the environmental stability of a typical acrylate resist. T-topping is evident after 30 minutes in an environment with 0.6 ppb of ammonia and 0.08 ppb of N-methyl pyrilodone (NMP). At much longer time frames (60 minutes or greater), these structures experience space closure and catastrophic failure. 

Uncertainty analysis was mentioned many times at the workshop, and still to come are multiscale systems, fully stochastic systems, and so on. And then we will move toward design optimization and optimal control. There is a need for more and better software tools in this area. Even further in the future will be computational design of experiments, with the challenge of learning the extent to which one can learn something from incomplete information. Where should the experiment be done Where does the most predictive power exist in experiment space and physical space Right now, these questions are commonly answered by intuition, and some experimentalists are tremendonsly good at it, but computations will be able to help. Some examples are shown in Box 3. 

Voyager mission photopolarimeter experiment. Space Science Review, 21,159-81. Limaye, S. S. (1986). Jupiter new estimates of the mean zonal flow at the cloud level. 

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