Distribution-Free Multivariate Process Control Based On Log-Linear Modeling

摘要

This paper considers statistical process control (SPC) when the process measurement is multivariate. In the literature, most existing multivariate SPC procedures assume that the in-control distribution of the multivariate process measurement is known and it is a Gaussian distribution. In applications, however, the measurement distribution is usually unknown and it needs to be estimated from data. Furthermore, multivariate measurements often do not follow a Gaussian distribution (e.g., cases when some measurement components are discrete). We demonstrate that results from conventional multivariate SPC procedures are usually unreliable when the data are non-Gaussian. Existing statistical tools for describing multivariate non-Gaussian data, or, transforming the multivariate non-Gaussian data to multivariate Gaussian data are limited, making appropriate multivariate SPC difficult in such cases. In this paper, we suggest a methodology for estimating the in-control multivariate measurement distribution when a set of in-control data is available, which is based on log-linear modeling and which takes into account the association structure among the measurement components. Based on this estimated in-control distribution, a multivariate CUSUM procedure for detecting shifts in the location parameter vector of the measurement distribution is also suggested for Phase Ⅱ SPC. This procedure does not depend on the Gaussian distribution assumption; thus, it is appropriate to use for most multivariate SPC problems.