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10 2 performing a 2 k factorial design.
2 5 factorial design example. The advantage of factorial design becomes more pronounced as you add more factors. The interaction used to generate the 1 2 fraction is called the generator of the fractional factorial design. To perform a factorial design. Let s imagine a design where we have an educational program where we would like to look at a variety of program variations to see which works best.
Slow 05 mm and fast 125 mm factor 3 wheel grit 2 levels. This design is called a quarter fraction of the full 2 5 or a 2 5 2 design a two to the five minus two design. Hunter new york john wiley sons 1978 and also given in the book design and analysis of experiments 5th edition by. There are very useful summaries of two level fractional factorial designs for up to 11 factors originally published in the book statistics for experimenters by g e p.
4 7 incomplete block designs. Factorial designs a simple example. We will discuss designs where there are just two levels for each factor. A 1 2 fraction can be generated from any interaction but using the highest order interaction is the standard.
For example with three factors the factorial design requires only 8 runs in the form of a cube versus 16 for an ofat experiment with equivalent power. A full factorial for the five factors a b c d e would have needed 2 5 32 runs. Useful fractional factorial designs for up to 10 factors are summarized here. Slow 025 m s and fast 125 m s factor 2 down feed rate 2 levels.
6 2 estimated effects and the sum of squares from the contrasts. Probably the easiest way to begin understanding factorial designs is by looking at an example. For instance we would like to vary the amount. Number of observations 32 a complete 2 5 factorial design response variable y mean over 15 reps of ceramic strength factor 1 table speed 2 levels.
6 3 unreplicated 2 k. The 2 k factorial design. Factors can be quantitative or qualitative. 6 1 the simplest case.
5 2 another factorial design example cloth dyes. Only 1 4 were run. Thus we want to run a 1 2 fraction of a 25 design. In both designs shown at the bottom.
Select a fixed number of levels of each factor. 5 1 factorial designs with two treatment factors. This design is called a 25 1 fractional factorial design.
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