Using a genetic algorithm to generate D‐optimal designs for mixture‐process variable experiments

This article presents and develops a genetic algorithm (GA) to generate D‐efficient designs for mixture‐process variable experiments. It is assumed the levels of a process variable are controlled during the process. The GA approach searches design points from a set of possible points over a continuo...

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Bibliographic Details
Published in:Quality and reliability engineering international 2019-12, Vol.35 (8), p.2657-2676
Main Authors: Pradubsri, Wasinee, Chomtee, Boonorm, Borkowski, John J.
Format: Article
Language:English
Subjects:
D‐optimality
Exchanging
genetic algorithm
Genetic algorithms
mixture experiment
Process controls
process variable
Process variables
Variance
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Summary:This article presents and develops a genetic algorithm (GA) to generate D‐efficient designs for mixture‐process variable experiments. It is assumed the levels of a process variable are controlled during the process. The GA approach searches design points from a set of possible points over a continuous region and works without having a finite user‐defined candidate set. We compare the performance of designs generated by the GA with designs generated by two exchange algorithms (DETMAX and k‐exchange) in terms of D‐efficiencies and fraction of design space (FDS) plots which are used to evaluate a design's prediction variance properties. To illustrate the methodology, examples involving three and four mixture components and one process variable are proposed for creating the optimal designs. The results show that GA designs have superior prediction variance properties in comparison with the DETMAX and k‐exchange algorithm designs when the design space is the simplex or is a highly‐constrained subspace of the simplex.
ISSN:0748-8017
1099-1638
DOI:10.1002/qre.2549