Statistical monitoring of multi-stage processes based on engineering models

Abstract

Most manufacturing processes consist of a large number of stages. The modeling of multi-stage processes by considering physical and mechanical laws in a linear state space form is extensively reported in the literature. This type of modeling describes the quality linkage among stages. However, recent research on statistical monitoring of multi-stage processes usually makes no use of this type of approach. A Statistical Process Control (SPC) method is proposed for multi-stage processes described by an engineering state space model. As a part of Phase I SPC analysis, a maximum likelihood estimation procedure based on an EM algorithm is developed. The complex multi-stage monitoring problem is converted to a simple multi-stream monitoring problem by applying group exponential weighted moving average charts to the one-step ahead forecast errors of the model. Reported run length results show the efficiency of the proposed charting method. The effectiveness of the proposed monitoring method is illustrated by its application to data from automobile hood manufacturing and workpiece assembly.

Keywords:

• Multi-stage process
• linear state space model
• EM algorithm
• group charts

Acknowledgements

The authors are grateful to the editor, the department editor, and the anonymous referees for their valuable comments. Also, special thanks to Yi Zhao and Changliang Zhou for their help in the simulation studies. This research was supported by RGC Competitive Earmarked Research Grants 620405 and 620606.