Recent work on multistratum fractional factorial designs is set in a general and unified framework, and a criterion for selecting multistratum fractional factorial designs that takes stratum variances into account is proposed. Application of the general theory is illustrated on designs of experiments with multiple processing stages, including split-lot designs, blocked strip-plot designs, and p...

Non-regular two-level fractional factorial designs, such as Plackett–Burman designs, are becoming popular choices in many areas of scientific investigation due to their run size economy and flexibility. The run size of nonregular two-level factorial designs is a multiple of 4. They fill the gaps left by the regular twolevel fractional factorial designs whose run size is always a power of 2 (4, ...

Two-level factorial and fractional factorial designs have played a prominent role in the theory and practice of experimental design. Though commonly used in industrial experiments to identify the significant effects, it is often undesirable to perform the trials of a factorial design (or, fractional factorial design) in a completely random order. Instead, restrictions are imposed on the randomi...

Fractional factorial designs are used widely in screening experiments to identify significant effects. It is not always possible to perform the trials in a complete random order and hence, fractional factorial split-plot designs arise. In order to identify optimal fractional factorial split-plot designs in this setting, the Hellinger distance criterion (Bingham and Chipman (2007)) is adapted. T...

Two designs for a fractional factorial experiment are equivalent if one can be obtained from the other by reordering the treatment combinations, relabeling the factors and relabeling the factor levels. Designs can be viewed as sets of points in pdimensional space, where p is the number of factors. It is shown that, in this setting, two designs are equivalent if the Hamming distances between the...

Multi-level factorial designs are useful in experiments but their aliasing structure are complex compare to two-level fractional factorial designs. A new framework is proposed to study the complex aliasing of those designs. Geometric aliasing is deened for factorial designs. It generalize of the aliasing relation of regular two level fractional fac-torial designs to all factorial designs. Based...

The joint use of counting functions, Hilbert basis and Markov basis allows to define a procedure to generate all the fractions that satisfy a given set of constraints in terms of orthogonality. The general case of mixed level designs, without restrictions on the number of levels of each factor (like primes or power of primes) is studied. This new methodology has been experimented on some signif...

Regular two-level fractional factorial designs are often used in industrial experiments as screening experiments. When some factors have levels which are hard or expensive to change, restrictions are often placed on the order in which runs can be performed, resulting in a split-plot factorial design. In these cases, the hard or expensive to change factors are applied to whole plots, whereas the...