On modeling of variability in mixture experiments with noise variables

TL;DR

This paper compares the delta method and joint modeling of mean and dispersion for analyzing variability in mixture experiments with uncontrollable noise variables, aiming to improve quality control.

Contribution

It introduces an alternative approach using joint modeling of mean and dispersion alongside the delta method for mixture experiments with noise variables.

Findings

Both methods effectively model mean and variance.

Joint modeling provides a flexible alternative to the delta method.

Optimization reduces variability while maintaining target mean.

Abstract

In mixture experiments with noise variables or process variables that can not be controlled, investigate and try to control the variability of the response variable is very important for quality improvement in industrial processes. Thus, modeling the variability in mixture experiments with noise variables becomes necessary and has been considered in literature with approaches that require the choice of a quadratic loss function or by using the delta method. In this paper, we make use of the delta method and also propose an alternative approach, which is based on the Joint Modeling of Mean and Dispersion (JMMD). We consider a mixture experiment involving noise variables and we use the techniques of JMMD and of the delta method to get models for both mean and variance of the response variable. Following the Taguchi's ideas about robust parameter design we build and solve an optimization problem for minimizing the variance while holding the mean on the target. At the end we provide a discussion about the two methodologies considered.