In a general fractional factorial design the n levels of each factor are coded by the n-th roots of the unity. This device allows a full generalization to mixed designs of the theory of polynomial indicator function already introduced for binary designs by Fontana and the Authors (2000). Properties of orthogonal arrays and regular fractions are discussed.

Fractional factorial designs are widely used in practice and typically chosen according to the minimum aberration criterion. A sequential algorithm is developed for constructing efficient fractional factorial designs. A construction procedure is proposed that only allows a design to be constructed from its minimum aberration projection in the sequential build-up process. To efficiently identify...

Data screening is an indispensable phase in initiating the scientific discovery process. Fractional factorial designs offer quick and economical options for engineering highly-dense structured datasets. Maximum information content is harvested when a selected fractional factorial scheme is driven to saturation while data gathering is suppressed to no replication. A novel multi-factorial profile...

This article addresses the varied possibilities for following a two-level fractional factorial with another fractional factorial half the size of the original experiment. While follow-up fractions of the same size as an original experiment are common practice, in many situations a smaller follow-up experiment will suffice. Peter John coined the term “semifolding” to describe using half of a fol...

Discrete choice experiments (DCEs) are increasingly used for studying and quantifying subjects preferences in a wide variety of healthcare applications. They provide a rich source of data to assess real-life decision-making processes, which involve trade-offs between desirable characteristics pertaining to health and healthcare and identification of key attributes affecting healthcare. The choi...

This note builds on results from Wu, Mee and Tang‘s (2012) article (henceforth WMT) on admissible fractional factorial two-level designs, specifically concentrating on the “dominating designs” that have been introduced but not further pursued in WMT. WMT’s work has been used for increasing the efficiency of the author’s graph-based algorithm for creation of minimum aberration designs that keep ...

Identities about the wordlength patterns of regular s designs and their complementary designs are established through a first-order differential equation satisfied by a structure function. The identities are then generalized to s designs with multiple groups of factors. An advantage of using the structure function and partial differential equation is that it can easily adapt to some structural ...

In unreplicated 2kp designs, the assumption of constant variance is commonly made. When the variance of the response differs between the two levels of a column in the effect matrix, that column produces a dispersion effect. In this article we show that two active dispersion effects may create a spurious dispersion effect in their interaction column. Most existing methods for dispersion-effect t...