Model Robust Response Surface Designs: Scaling Two-Level Factorials.
Abstract
In response surface methodology, carefully designed experiments are used to study the relationship between an experimental response variable and a set of continuous explanatory variables. The experiments are designed to permit estimation of the parameters of a simple graduating function which, it is tentatively assumed, will provide a reasonable approximation to the true response function. These designs usually involve only a few levels of each explanatory variable, so the experimenter must decide how far apart to choose the levels. If the levels are too close together, estimates from the model will have high variance, but if the levels are too far apart, the graduating function may no longer adequately approximate the true response function, leading to large bias errors. An effective resolution of these conflicting demands must depend on the experimenter's beliefs as to the adequacy of the graduating function. Bayesian statistical methods allow us to formulate a model that includes explicit assumptions about the experimenter's beliefs. The author formulated an experimental design criterion based on such a model and studies the implications of the criterion for scaling two-level factorial experiments, which are often used when the graduating function is a first degree polynomial. It is shown that the criterion leads to reasonable choices of scale that are not highly sensitive to the experimenter's beliefs.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1984
- Accession Number
- ADA147494
Entities
People
- D. M. Steinberg
Organizations
- University of Wisconsin–Madison