Economic Trend Free Blocked Full 2^k Factorial Experiments

Abstract

This article considers blocking full 2k factorial experiments one-block- at-a-time into {1,2,4,8,...2k−1} blocks such that all factor main effects (A1, A2, A3, . . . Ak) are resistant to the polynomial time trend, which might be present in the sequentially generated responses while keeping blocking factors confounded with negligible high order interactions. Cost of factor level changes between successive runs within blocks is also minimized. For each blocked 2k design we provide the following: (i) the independent block- ing factors as negligible high order interactions (ii) the number of factor level changes (i.e., cost) in each block and the total cost of factor level changes in all blocks and (iii) the k independent Generalized Foldover run genera- tors to sequence all 2k runs of the full 2k factorial experiment within each block one-run-at-a-time, where (k − i) generators are within blocks genera- tors while i are between blocks generators (i = 0, 1, 2, . . . k − 1), where i = 0 for no blocking, i = 1 for blocking into 2 blocks, i = 2 for blocking into 4 blocks, . . . i = (k − 1) for blocking into 2k−1 blocks. Proposed general block- ing results have been derived inductively using extensive computer work on blocking trend free full 2k factorial experiments for k = 4, 5, 6, . . . 15 factors. Keywords: Systematic factorial experiments, Generalized Foldover Scheme for runs sequencing, Cost of factor level changes, Factors’ time trend resis- tance, Blocking factors and their confounding structure.