Search results
Results from the WOW.Com Content Network
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 ...
A fractional factorial design is said to have resolution if every -factor effect [note 5] is unaliased with every effect having fewer than factors. For example, a design has resolution R = 3 {\displaystyle R=3} if main effects are unaliased with each other (taking p = 1 ) {\displaystyle p=1)} , though it allows main effects to be aliased with ...
= 3×5! + 4×4! + 1×3! + 0×2! + 1×1! + 0×0! = ((((3×5 + 4)×4 + 1)×3 + 0)×2 + 1)×1 + 0 = 463 10. (The place value is the factorial of one less than the radix position, which is why the equation begins with 5! for a 6-digit factoradic number.) General properties of mixed radix number systems also apply to the factorial number system.
1.328: 5 circles inversion fractal: The limit set generated by iterated inversions with respect to 5 mutually tangent circles (in red). Also an Apollonian packing. See [15] 1.36521 [16] Quadratic von Koch island using the type 1 curve as generator: Also known as the Minkowski Sausage: Calculated: 1.3934: Douady rabbit
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 ...
The interaction of two factors with s 1 and s 2 levels, respectively, has (s 1 −1)(s 2 −1) degrees of freedom. The formula for more than two factors follows this pattern. In the 2 × 3 example above, the degrees of freedom for the two main effects and the interaction — the number of columns for each — are 1, 2 and 2, respectively.
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;