This paper simplifies a previous exposition of Rao’s 1947 proof of his inequalities for orthogonal arrays. A key issue in the proof is the way in which one defines effects in a fractional factorial design. Here we replace the definition used in the earlier exposition with a simpler one, based on a more obvious interpretation of what Rao wrote and more in line with common practice, and show that...

Nonregular fractional factorial designs such as Plackett-Burman designs are widely used in industrial experiments for run size economy and flexibility. A novel criterion, called moment aberration projection, is proposed to rank and classify nonregular designs. It measures the goodness of a design through moments of the number of coincidences between the rows of its projection designs. The new c...

A commonly used follow-up experiment strategy involves the use of a foldover design by reversing the signs of one or more columns of the initial design. DeŽ ning a foldover plan as the collection of columns whose signs are to be reversed in the foldover design, this article answers the following question: Given a 2kp design with k factors and p generators, what is its optimal foldover plan? We ...

This contribution presents an overview of sensitivity analysis of simulation models, including the estimation of gradients. It covers classic designs and their corresponding (meta)models; namely, resolution-III designs including fractional-factorial twolevel designs for …rst-order polynomial metamodels, resolution-IV and resolution-V designs for metamodels augmented with twofactor interactions,...

Considering general prime or prime powered factorials, we give a nite projective geometric formulation for regular fractional factorial split-plot designs. This provides a uniied framework for such designs and facilitates their systematic study under the criteria of minimum aberration and minimum secondary aberration; the latter criterion is introduced to achieve ner discrimination. We investig...

1. In poultry investigations, the main interest is often to study the effects of many factors simultaneously. Two or three level factorial designs are the most commonly used for this type of investigation. However, it is often too costly to perform when number of factors increase. So a fractional factorial design, which is a subset or a fraction of a full factorial design, is an alternative. Th...

Many disorders require multi-component treatments given sequentially in time to achieve and maintain good outcomes. The development of these adaptive treatment strategies is challenging due to the large number of components and sequencing of components. We propose the use of screening experiments in which scientists screen out inactive components. Unfortunately when the goal is to construct ada...

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