The non-parametric approach to the quantification of the uncertainty in the design of experiments modelling

Abstract

The classic design of experiments (DoE) typically uses the least-square method for a model identification and requires associated assumption about the normality of a noise factor. It is very convenience because it leads to a relative simple computations and well-known asymptotic statistics based on the normality assumption. However, if that assumption is not satisfied it may fail and obtained results may differ radically from the verification tests. The rationale for the caution may be the comparison of interval plots (based on the normality hypothesis) and box-plots (based on raw data). The useful approach is the bootstrap-based methodology which replaces the requirement of the normality assumption with weaker requirement of the independent and identical distribution (i.i.d.) of the random term. The industrial applications of this approach are still rare because the industry is very conservative and usually utilizes old well-known methods and typical numerical software like e.g. Statistica, Statgraphics or Minitab. This paper presents the bootstrap modeling of the random uncertainty in the two cases: The factorial designed experiment and the response surface experiment.