5.7.4. DOE Methods
Full Factorial Design
If three factors (design variables) such as A, B and C have two-level, then the full factorial design is a combination of 2^3. If the factors have 3-level for all design variables, then the full factorial design is a combination of 3^3. However, in order to help to generate more detailed DOE result table, RecurDyn supports that the user can define the level of each design variable separately. So, if the factor A has 2-level, B has 4-level, and C has 3-level, then the full factorial design is a combination of 2*4*3. For the limitations, please refer to the Table 5.15.
2 Level Full Factorial Design
2 Level Full Factorial Design is the special case of Full Factorial Design, and it is a common experimental design. When the user selects the 2 Level Full Factorial Design, all the design variables are assumed as two-level although the users define the level of each factor with other levels. For the limitations, please refer to the Table 5.15.
2 Level Plackett-Burman Design
In 1946, R.L. Plackett and J.P. Burman published their paper “The Design of Optimal Multifactorial Experiments” in Biometrika (vol. 33). Plackett-Burman designs are very efficient screening designs when only main effects are of interest. This method is assumed as 2 level and it is recommended when the users want to find the main factors among large number of factors. In this method, the number of trial conditions expands by multiples of four. For the limitations, please refer to the Table 5.15.
Central Composite Design
A Box-Wilson Central Composite Design, commonly called “a central composite design”, contains an imbedded factorial or fractional factorial design with center points that is augmented with a group of “star points” that allow estimation of curvature. If the distance from the center of the design space to a factorial point is ±1 unit for each factor, the distance from the center of the design space to a star point is ±α with |α| > 1 as shown in Figure 5.66. The precise value of α depends on certain properties desired for the design and on the number of factors involved. For the limitations, please refer to the Table 5.15.
Figure 5.66 Generation of a Central Composite Design for Two Factors and Comparison of the Three Types of Central Composite Designs
Box-Behnken Design
The Box-Behnken design is an independent quadratic design in that it does not contain an embedded factorial or fractional factorial design. In this design the treatment combinations are at the midpoints of edges of the process space and at the center as shown in Figure 5.67. This method is assumed as 3 level for each factor. For the limitations, please refer to the Table 5.15.
Figure 5.67 A Box-Behnken Design for Three Factors
Latin-Hypercube Sampling
The Latin Hypercube sampling is developed as a variance reduction technique or as a screening technique. The basic of Latin Hypercube sampling is a full stratification of sampled distribution with a random selection inside each stratum. The sample values are randomly shuffled among different variables. The Latin Hypercube sampling has been widely used in the deterministic simulation for computer experimentation. Also, this is recommended a space filling sampling for constructing meta-model. For the limitations, please refer to the Table 5.15.
Figure 5.68 A Latin Hypercube sample with Runs(N)=6 and number of factors = 2
Level |
nMinDV |
nMaxDV |
nMaxRun |
|
FFD |
Free User Input |
1 |
19 |
|
2LFFD |
3 |
1 |
19 |
|
2LPBD |
2 |
1 |
100 |
|
CCD |
3 |
1 |
19 |
|
BBD |
3 |
3 |
100 |
|
LHS |
Automatic |
1 |
100 |
1,000 |
[Ref] http://www.itl.nist.gov/div898/handbook