Robust Parameter Designs for Reducing Effects of Noise Covariates: A Performance Measure Approach

Abstract

We consider a methodology of robust parameter designs in order to reduce effects of noise variables which are random covariates, not designed values of noise factors. This problem setting is discussed in a few previous works whose design procedures are not based on a certain performance measure but on results of statistical tests of control-by-noise interaction effects which depends on the assumption of the normality in the Gaussian linear regression model. On the other hand, we introduce a model including a bounded nonlinear function, define a signal-to-noise ratio, which is a popular performance measure in the case of compound noise experiments, and propose a design procedure using this performance measure. Additionally, based on the asymptotic normality of least squares estimators for the model parameters, we provide a consistent test which corresponds to the tests in the previous works.