Article: Mixture-process variable experiments including control and noise variables within a split-plot structure Journal: International Journal of Quality Engineering and Technology (IJQET) 2011 Vol.2 No.1 pp.1 - 28 Abstract: In mixture-process variables experiments, it is common that the experimental runs are larger than the mixture only design or basic experimental design to estimate the increased coefficient parameters due to the mixture components, process variable, and interaction between mixture and process variables, some of which are hard to change or cannot be controlled under normal operating condition. These situations often prohibit a complete randomisation for the experimental runs due to the time or financial reason. These types of experiments can be analysed in a model for the mean response and a model for the slope of the response within a split-plot structure. When considering the experimental designs, low prediction variances for the mean and slope model are desirable. We demonstrate the methods for the mixture-process variable designs with noise variables considering a restricted randomisation and evaluate some mixture-process variable designs that are robust to the coefficients of interaction with noise variables using fraction of design space plots with the respect to the prediction variance properties. Finally, we create the G-optimal design that minimises the maximum prediction variance over the entire design region using a genetic algorithm. Inderscience Publishers - linking academia, business and industry through research

Title: Mixture-process variable experiments including control and noise variables within a split-plot structure

Authors: Tae-Yeon Cho, Connie M. Borror, Douglas C. Montgomery

Addresses: Arizona State University, Tempe, Arizona 85287, USA. ' Arizona State University West, Phoenix, Arizona 85069, USA. ' Arizona State University, Tempe, Arizona 85287, USA

Abstract: In mixture-process variables experiments, it is common that the experimental runs are larger than the mixture only design or basic experimental design to estimate the increased coefficient parameters due to the mixture components, process variable, and interaction between mixture and process variables, some of which are hard to change or cannot be controlled under normal operating condition. These situations often prohibit a complete randomisation for the experimental runs due to the time or financial reason. These types of experiments can be analysed in a model for the mean response and a model for the slope of the response within a split-plot structure. When considering the experimental designs, low prediction variances for the mean and slope model are desirable. We demonstrate the methods for the mixture-process variable designs with noise variables considering a restricted randomisation and evaluate some mixture-process variable designs that are robust to the coefficients of interaction with noise variables using fraction of design space plots with the respect to the prediction variance properties. Finally, we create the G-optimal design that minimises the maximum prediction variance over the entire design region using a genetic algorithm.

Keywords: fraction of design space; FDS; genetic algorithms; GAs; noise variables; mixture-process variable experiments; quality engineering; robust design; parameter design; optimal design; split-plot design; experimental design.

DOI: 10.1504/IJQET.2011.038719

International Journal of Quality Engineering and Technology, 2011 Vol.2 No.1, pp.1 - 28

Published online: 21 Feb 2015 *

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Title: Mixture-process variable experiments including control and noise variables within a split-plot structure

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