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How to construct a fractional factorial design

We can include as many variables as there are columns in X In this chapter we shall use bold-face arabic numeral characters to denote the variable columns in the matrices. This has practical consequences as we shall see later on. [Pg.125]

Example-. A two-variable factorial design has the following complete model matrix [Pg.125]

The column 12 is to be read as the product of 1 2. We can use the colums 1, 2, 12 to define the variation of three variables, x, x, x in four runs and this gives the design matrix [Pg.125]

This is one half-fraction of a complete three-variable factorial design and it is seen that the experiments correspond to Exp no 5, 2, 3, 8 in the complete factorial design. Fig. 6.1 shows how the experiments of the half-fraction are distributed in the space spanned by the three variables. [Pg.125]

It is seen that the experimental points describe a tetrahedron, which is the largest volume of the space which can be spaimed by only four points. This shows an important property of fractional factorial designs the experiments cover as large a part as possible of the space spanned by the variables. We cannot cover the whole space by a limited number of points, but a fractional factorial design selects experiments which are as widely distributed as possible and which hence do their best to cover a maximum variation over the experimental space. [Pg.126]


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