Response surface designs and analysis for bi-randomization error structures

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Virginia Tech

Cost control, resource availability, or difficulty in performing complete randomizations may dictate the necessity to run response surface experiments in a bi-randomization error control format of which the split plot design is a special case. A bi-randomization scheme allows for certain factor levels to be applied at random to large experimental units with the remaining factor levels randomly applied to nested smaller units. For example, in the dual response surface approach to robust parameter design, process mean and variance models are formulated to aid in designing products to be "robust" to uncontrollable system influences called noise variables. In model development, noise variables are assumed to be controllable in the laboratory, but due to their random nature they may be costly and/or difficult to control. This suggests the need for a bi-randomization scheme in which the noise variables constitute the levels applied to the larger experimental units.

For the bi-randomization situation, two types of bi-randomization designs are explored along with their respective analyses and various error variance estimation procedures. The efficiency of common response surface designs are also examined in the presence of this alternative error structure to determine the necessity of design modifications to better accommodate the error structure. General recommendations for efficient designs and practical analysis methods are outlined.