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Optimal additions to and deletions from two‐level orthogonal arrays
Author(s) -
Butler Neil A.,
Ramos Victorino M.
Publication year - 2007
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2007.00576.x
Subject(s) - orthogonal array , mathematics , class (philosophy) , type (biology) , combinatorics , fractional factorial design , factorial experiment , mathematical optimization , computer science , statistics , taguchi methods , artificial intelligence , ecology , biology
Summary. Consider the problem of selecting a two‐level factorial design. It is well known that two‐level orthogonal arrays of strength 4 or more with e extra runs have various optimality properties including generalized Cheng (type 1) optimality when e =1, restricted Cheng (type 1) optimality when e =2 and E ‐optimality when 3 e 5. More general Schur optimality results are derived for more general values of e within the more restricted class of augmented two‐level orthogonal arrays. Similar results are derived for the class of orthogonal arrays with deletions. Examples are used to illustrate the results and in many cases the designs are confirmed to be optimal across all two‐level designs.