5.
Process Improvement
5.3. Choosing an experimental design 5.3.3. How do you select an experimental design?
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Three-level designs are useful for investigating quadratic effects | The three-level design is written as a 3k factorial design. It means that k factors are considered, each at 3 levels. These are (usually) referred to as low, intermediate and high levels. These levels are numerically expressed as 0, 1, and 2. One could have considered the digits -1, 0, and +1, but this may be confusing with respect to the 2-level designs since 0 is reserved for center points. Therefore, we will use the 0, 1, 2 scheme. The reason that the three-level designs were proposed is to model possible curvature in the response function and to handle the case of nominal factors at 3 levels. A third level for a continuous factor facilitates investigation of a quadratic relationship between the response and each of the factors. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Three-level design may require prohibitive number of runs | Unfortunately, the three-level design is prohibitive in terms of the number of runs, and thus in terms of cost and effort. For example a two-level design with center points is much less expensive while it still is a very good (and simple) way to establish the presence or absence of curvature. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
The 32 design | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
The simplest 3-level design - with only 2 factors |
This is the simplest three-level design. It has two factors, each at
three levels. The 9 treatment combinations for this type of design
can be shown pictorially as follows:
FIGURE 3.23 A 32 Design Schematic
A notation such as "20" means that factor A is at its high level (2) and factor B is at its low level (0). |
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The 33 design | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
The model and treatment runs for a 3 factor, 3-level design |
This is a design that consists of three factors, each at three levels.
It can be expressed as a 3 x 3 x 3 = 33 design. The model for
such an experiment is
![]() In this model we see that i = 1, 2, 3, and similarly for j and k, making 27 treatments. |
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Table of treatments for the 33 design |
These treatments may be displayed as follows:
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Pictorial representation of the 33 design |
The design can be represented pictorially by
FIGURE 3.24 A 33 Design Schematic
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Two types of 3k designs |
Two types of fractions of 3k designs are employed:
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