Minimum Cost Trend-Free 2n−(n−k)Fractional Factorial Designs of Resolution IV Derivable from the Normalized Sylvester-Hadamard Matrices

Autor: Guiatni, Ahlam, Hilow, Hisham
Zdroj: Journal of Statistical Theory and Practice; March 2023, Vol. 17 Issue: 1
Abstrakt: This article utilizes the normalized Sylvester-Hadamard 2k× 2kmatrices of order 2kand their associated saturated orthogonal arrays OA(2k, 2k− 1, 2, 2) in (2k− 1) factors to construct (by factor projection) two categories of economic systematic 2n−(n−k)designs of resolution IV: (i) minimum cost fractional factorial 2n−(n−k)designs (2k−2≤ n≤ 2k−1) (ii) minimum cost linear trend-free fractional factorial 2n−(n−k)designs (2k−2≤ n≤ (2k−1–2)), where each systematic 2n−(n−k)design is economic and allows for the estimation of all factor main effects unbiased by the linear time trend or by non-negligible two-factor interactions. The article provides for each proposed 2n−(n−k)design: (i) the kindependent generators to sequence its 2n−(n−k)runs by the generalized foldover scheme to minimize the cost of factor level changes between successive runs and (ii) the minimum total cost of factor level changes between the 2n−(n−k)successive runs. Proposed systematic 2n−(n−k)designs compete well and are better than existing systematic 2n−(n−k)designs cost-wise and trend resistance-wise.
Databáze: Supplemental Index
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