Monitoring General Linear Profiles Using Multivariate Exponentially Weighted Moving Average Schemes

TLDR

The authors propose a statistical process control scheme that employs a multivariate exponentially weighted moving average to monitor general linear profiles in industrial processes. The scheme builds on the general linear profile model, incorporates variable sampling intervals and a parametric diagnostic approach, and is demonstrated on a deep reactive ion etching semiconductor example.

Abstract

We propose a statistical process control scheme that can be implemented in industrial practice, in which the quality of a process can be characterized by a general linear profile. We start by reviewing the general linear profile model and the existing monitoring methods. Based on this, we propose a novel multivariate exponentially weighted moving average monitoring scheme for such a profile. We introduce two other enhancement features, the variable sampling interval and the parametric diagnostic approach, to further improve the performance of the proposed scheme. Throughout the article, we use a deep reactive ion etching example from semiconductor manufacturing, which has a profile that fits a quadratic polynomial regression model well, to illustrate the implementation of the proposed approach.