The Empirical Assessment of the Convergence Rate for the Bootstrap Estimation in Design of Experiment Approach

Abstract

Design of experiment (DoE) is a set of practical recipes and theoretical assumptions leading to the optimization of the technological process and/or the stabilization of its output quality. Practically, all the DoE approaches assume the normality of a random noise and the quasi-linearity of models taken from the general linear model (GLM) class. It allows to use traditional least-square methodology to identification of a model parameters and their confidence intervals. It gives usually sufficient results but completely fails if the model is not from GLM class or a random noise has not a normal distribution. The solution for such problems is the bootstrap approach, a resampling method based on Monte Carlo strategies. This paper tries to answer a question how many repetitions should be made to estimate parameters of the prediction model with sufficient accuracy.