A novel technique for constructing nonregular nine-level designs: Adjusted multiple tripling technique

Abstract

Nonregular designs are becoming popular and preferred choices in many areas of scientific investigation for their flexibility and run size economy. The lack of simple design structure is one of the significant obstacles for the use of nonregular designs, especially for experiments with high-level factors. While the construction of nonregular low-level designs is soundly investigated, few work are devoted to discuss nonregular high-level designs. The multiple tripling (MT) technique (Elsawah, J Comput Appl Math 384:113164, 2021) has been proposed as a new effective method for constructing nonregular three-level designs. This paper gives an adjusted MT technique for constructing a novel class of nonregular nine-level designs with simple design structure. The new nonregular nine-level designs fill the gaps left by the regular designs and thus are flexible in accommodation various combinations of factors, where the run sizes are a power of nine and a power of three for the regular designs and the new nonregular designs, respectively. Theoretical and numerical justifications for the good performance of the new designs are given based on various optimality criteria. Moreover, the modelling performance of the new designs is investigated. The results show that the new designs are better than the designs that can be generated using the existing R package.