A series of single array \(2^m\) factorial search designs for even \(m\). (English) Zbl 1336.62224
Summary: By means of a search design one is able to search for and estimate a small set of non-zero elements from the set of higher order factorial interactions in addition to estimating the lower order factorial effects. One may be interested in estimating the general mean and main effects, in addition to searching for and estimating a non-negligible effect in the set of 2- and 3-factor interactions, assuming 4- and higher-order interactions are all zero. Such a search design is called a ‘main effect plus one plan’ and is denoted by MEP.1. Construction of such a plan, for \(2^m\) factorial experiments, has been considered and developed by several authors and leads to MEP.1 plans for an odd number \(m\) of factors. These designs are generally determined by two arrays, one specifying a main effect plan and the other specifying a follow-up. In this paper we develop the construction of search designs for an even number of factors \(m\), \(m\neq 6\). The new series of MEP.1 plans is a set of single array designs with a well structured form. Such a structure allows for flexibility in arriving at an appropriate design with optimum properties for search and estimation.
References:
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