Partially replicated three-level designs via one-third foldover

Partially replicated factorial designs are widely used in experimental design, since they not only save experimental costs, but also effectively estimate the experimental error variance. In this paper, a method of constructing three-level fractional factorial designs with partially replicated runs is proposed based on one-third foldover techniques, and the properties of constructed partially replicated designs are investigated by indicator functions. First, based on the link between the indicator functions of partially replicated three-level designs and their initial designs, the necessary and sufficient 条件 for the constructed partially replicated three-level designs of re解 III.c or IV.c are explored. Second, an algorithm is provided to search for the optimal partially replicated three-level designs with maximum re解 in this paper. The algorithm is applied to initial designs of several regular and nonregular cases with 4, 5, and 6 factors, respectively. For these initial designs, partially replicated three-level designs with maximum re解 are obtained for practice. Finally, a case of control valve experiments is studied, and the analysis of variance of real data from a seat belt experiment between three-level partially replicated designs and orthogonal designs is compared under the same run size. The results show that partially replicated designs can effectively improve the estimation of factor effects and achieve a better estimation performance in experiments with the same scale.