An efficient methodology for constructing optimal foldover designs in terms of mixture discrepancy

Abstract

Available online xxxx AMS 2000 subject classifications: 62K05 62K15 Keywords: Mixture discrepancy criterion Foldover plan Foldover design Combined design Balanced design Lower bound a b s t r a c t Mixture discrepancy criterion (Zhou et al., 2013) is more reasonable than other discrepancies criteria for measuring the uniformity of experimental designs. In this paper, we take the mixture discrepancy criterion as the optimality measure to assess optimal foldover plans, which serve as benchmarks for constructing optimal foldover and combined designs (see Definition 2). New analytical expressions as well as new lower bounds of the mixture discrepancy criterion for both symmetric two-level and three-level combined designs under general foldover plans are obtained. We also describe necessary conditions for the existence of optimal combined designs meeting these lower bounds. An algorithm for searching the optimal foldover plans is also developed. Illustrative examples are provided, where numerical studies lend further support to our theoretical results. These results may help to provide some powerful and efficient algorithms for searching the optimal foldover and combined designs.

A powerful and efficient algorithm for breaking the links between aliased effects in asymmetric designs

“…The mixture discrepancy criterion is more attractive than other discrepancy criteria for measuring uniformity. The purpose of the present paper is to extend the results in Elsawah & Qin (2016a) from symmetric fractional factorial designs to fractional factorial designs with a mixture of two and three levels. This article develops a new approach for constructing optimal combined designs with a mixture of two and three levels.…”

“…The purpose of the present paper is to extend the results in Elsawah & Qin () from symmetric FF designs to FF designs involving a mixture of factors with two and three levels. This article develops a new approach for constructing optimal combined designs with such mixtures.…”

“…In this section, we extend the mechanism for construction of foldover plans found in Elsawah & Qin () from symmetric FF designs to asymmetric FF designs as follows.…”

“…Subsequently, Elsawah & Qin (, ) discussed the construction of optimal symmetric two‐level and symmetric three‐level combined designs in the context of and criteria, respectively, and included a comparison study. Recently, Elsawah & Qin () studied optimal foldover plans in terms of the criterion for both symmetric two‐level and symmetric three‐level designs. Finally, Elsawah et al.…”

Optimum mechanism for breaking the confounding effects of mixed-level designs

“…Qin (2015b, 2016c) discussed the construction of optimal two-level and threelevel combined designs in view of all used uniformity criteria with a comparison study respectively. Recently, Elsawah and Qin (2016a) studied the issue of the optimal foldover plans in terms of mixture discrepancy for both two-level and three-level designs. Finally, Elsawah et al (2016) studied the issue of the optimal foldover plans for four-level designs in view of the CD.…”