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The results of that example may be used to simulate a fractional factorial experiment using a half-fraction of the original 2 4 = 16 run design. The table shows the 2 4-1 = 8 run half-fraction experiment design and the resulting filtration rate, extracted from the table for the full 16 run factorial experiment.
A fractional factorial design contains a carefully chosen subset of these combinations. The criterion for choosing the subsets is discussed in detail in the fractional factorial designs article. Formalized by Frank Yates , a Yates analysis exploits the special structure of these designs to generate least squares estimates for factor effects for ...
In a fractional factorial experiment, the contrast vectors belonging to a given effect are restricted to the treatment combinations in the fraction. Thus, in the half-fraction {11, 12, 13} in the 2 × 3 example, the three effects may be represented by the column vectors in the following table:
Designed experiments with full factorial design (left), response surface with second-degree polynomial (right) In statistics, a full factorial experiment is an experiment whose design consists of two or more factors, each with discrete possible values or "levels", and whose experimental units take on all possible combinations of these levels across all such factors.
Plackett–Burman designs are experimental designs presented in 1946 by Robin L. Plackett and J. P. Burman while working in the British Ministry of Supply. [1] Their goal was to find experimental designs for investigating the dependence of some measured quantity on a number of independent variables (factors), each taking L levels, in such a way as to minimize the variance of the estimates of ...
Designed experiments with full factorial design (left), response surface with second-degree polynomial (right) In statistics, response surface methodology (RSM) explores the relationships between several explanatory variables and one or more response variables. RSM is an empirical model which employs the use of mathematical and statistical ...
During World War II, a more sophisticated form of DOE, called factorial design, became a big weapon for speeding up industrial development for the Allied forces. These designs can be quite compact, involving as few as two levels of each factor and only a fraction of all the combinations, and yet they are quite powerful for screening purposes.
A factorial (perhaps fractional) design in the factors studied, each having two levels; A set of center points, experimental runs whose values of each factor are the medians of the values used in the factorial portion. This point is often replicated in order to improve the precision of the experiment;