Behavior factorial design

The saturated fractional factorial designs are satisfactory for exactly 3, or 7, or 15, or 31, or 63, or 127 factors, but if the number of factors is different from these, so-called dummy factors can be added to bring the number of factors up to the next largest saturated fractional factorial design. A dummy factor doesn t really exist, but the experimental design and data treatment are allowed to think it exists. At the end of the data treatment, dummy factors should have very small factor effects that express the noise in the data. If the dummy factors have big effects, it usually indicates that the assumption of first-order behavior without interactions or curvature was wrong that is, there is significant lack of fit. 

For systems involving many variables and levels it is apparent that a complete factorial design leads to an excessive number of cases. However, it may be quite practical to make reasonable assumptions about the behavior of the model and, in so doing, to reduce the number of cases... 

Another example concerns the optimization of micellar chromatography. Torres et al. [11] proposed a stepwise strategy, in which one starts with simple and very economic 2 factorial designs to optimize the separation at a constant pH, chosen on the basis of chemical expertise. Then if necessary one can introduce pH as an additional variable by expanding the design to 3 x 2 by carrying out two additional 2" designs. If still better description of the retention behavior is needed one can go to mechanistic models such as... 

Types that define the behavior expected at the interfaces to classes. Classes implement types. In some design styles, all parameters and variables are declared with types classes are referred to in the code only to instantiate new objects, and even that is encapsulated within factory objects. 

In the other two simple reinforcement schedules, reinforcement availability is based on the number of occurrences of the designated response. On an FR schedule, the completion of the number of responses specified by the schedule parameter value is required for each reinforcement delivery. An FR 100 schedule, then, requires 100 occurrences of the designated response for reinforcement delivery. The classic examples of FR schedules are the piecework systems that operated in factories early in US history, where workers were paid for each piece or unit they produced. The FR schedule generates its own characteristic behavior pattern which consists of a pause or period of no responding after each reinforcement delivery, followed by an abrupt transition to a very rapid rate of responding - a pattern known as break and run and shown in Figure 9. 

Mittal, V. 2008. Modeling the behavior of polymer-layered silicate nanocomposites using factorial and mixture designs. Journal of Thermoplastic Composite Materials 21 9-26. 

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