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A Stochastic Algorithm for Selecting of Defining Contrasts in Two‐Level Experiments
Author(s) -
Liao C.T.,
Iyer H.K.
Publication year - 1999
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/(sici)1521-4036(199910)41:6<671::aid-bimj671>3.0.co;2-o
Subject(s) - algorithm , set (abstract data type) , fractional factorial design , mathematical optimization , computer science , simple (philosophy) , factorial experiment , factorial , mathematics , machine learning , mathematical analysis , philosophy , epistemology , programming language
Franklin and Bailey (1977) provided an algorithm for construction of fractional factorial designs for estimating a user specified set of factorial effects. Their algorithm is based on a backtrack procedure. This is computer intensive when the number of factors is not small. We propose a stochastic search method called SEF (sequential elimination of factors) algorithm. The SEF algorithm is a simple modification of the exhaustive approach of the Franklin‐Bailey algorithm since defining contrasts for the design of interest are chosen stochastically rather than choosing them in a systematic and exhaustive manner. Our experience shows the probability of success of obtaining a required design to be sufficiently large to make this a practical approach. The success probability may be expected to be rather small if the required design is close to a saturated design. We suggest the use of this stochastic alternative particularly when the number of factors is large. This can offer substantial savings in computing time relative to an exhaustive approach. Moreover, if the SEF algorithm fails to produce a design even after several attempts, one can always revert back to the Franklin‐Bailey approach.