2 research outputs found
Enumeration of regular fractional factorial designs with four-level and two-level factors
Designs for screening experiments usually include factors with two levels
only. Adding a few four-level factors allows for the inclusion of multi-level
categorical factors or quantitative factors with possible quadratic or
third-order effects. Three examples motivated us to generate a large catalog of
designs with two-level factors as well as four-level factors. To create the
catalog, we considered three methods. In the first method, we select designs
using a search table, and in the second method, we use a procedure that selects
candidate designs based on the properties of their projections into fewer
factors. The third method is actually a benchmark method, in which we use a
general orthogonal array enumeration algorithm. We compare the efficiencies of
the new methods for generating complete sets of non-isomorphic designs.
Finally, we use the most efficient method to generate a catalog of designs with
up to three four-level factors and up to 20 two-level factors for run sizes 16,
32, 64, and 128. In some cases, a complete enumeration was infeasible. For
these cases, we used a bounded enumeration strategy instead. We demonstrate the
usefulness of the catalog by revisiting the motivating examples.Comment: 37 pages, 1 figure, 13 table
Design and analysis of a microplate assay in the presence of multiple restrictions on the randomization
Experiments using multi-step protocols often involve several restrictions on
the randomization. For a specific application to in vitro testing on
microplates, a design was required with both a split-plot and a strip-plot
structure. On top of two-level treatment factors and the factors that define
the randomization restrictions, a multi-level fixed blocking factor not
involving further restrictions on the randomization had to be added. We develop
a step-by-step approach to construct a design for the microplate experiment and
analyze a response. To consolidate the approach, we study various alternative
scenarios for the experiment.Comment: 31 pages, 13 tables, 4 figure