Toward identifying the source of mean shifts in multivariate SPC: a neural network approach

Abstract

To identify the source(s) of process shifts under a multivariate setting is a challenging problem. Though some statistical techniques have been proposed, they are limited or restricted in their level of success and ease of use. In this paper, we propose a neural-network based identifier (NNI) to detect process mean shifts as well as indicate the variable(s) responsible for the shifts in a process where variables are correlated. Various network configurations and training strategies were investigated to develop an effective network. This research demonstrates how the NNI with a simple network structure, i.e. without any hidden layers, can perform superiorly to the Hotelling T ² chart and comparably to the MEWMA chart in detecting small to moderate shifts for bivariate processes. The run length analysis also indicates that the NNI performs much more stably than the Hotelling T ² chart and the MEWMA chart. One of the great advantages of this approach is that the proposed identifier, aided with the NNI output chart, can indicate the source(s) of the shift(s), i.e. the variable(s) responsible for the shift(s). The NNI output chart allows this monitoring scheme to easily interpret the underlying structures of the process variables.

Keywords:

• Multivariate SPC
• Bivariate
• Control charts
• Hotelling T2 chart
• Neural networks
• Back-propagation

Acknowledgements

The author would like to thank the two referees for their valuable comments and suggestions, and Mr. Suresh K. Radhakrishnan for his computing support. This research was supported in part by National University of Singapore research grant No. R-314-000-060-112.