Construction of Blocked Factorial Designs to Estimate Main Effects and\n Selected Two-Factor Interactions

2019/07/04 by Janet Godolphin, Godolphin, Janet
Decision Sciences · Engineering · #05B05 #05C15 #62K10 #62K15 #Advanced optical system design #FOS: Mathematics #Optimal Experimental Design Methods #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1907.02373

openalex publication_date 2019/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Two-level factorial designs are widely used in industrial experiments. For\nprocesses involving (n ) factors, the construction of designs comprising\n (2ⁿ ) and (2^n-p ) factorials, arranged in blocks of size (2^q ) is\ninvestigated. The aim is to estimate all main effects and a selected subset of\ntwo-factor interactions. Designs constructed according to minimum aberration\ncriteria are shown to not necessarily be the most appropriate designs in this\nsituation. A design construction approach is proposed which exploits known\nresults on proper vertex colourings in graph theory. Examples are provided to\nillustrate the results and construction strategies.\n Particular consideration is given to the special case of designs with blocks\nof size four and tables of designs are given for this block size.\n

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