Optimizing a control plan using a structural equation model with an application to statistical process analysis

Abstract

In the case where non-experimental data are available from an industrial process and a directed graph for how various factors affect a response variable is known based on a substantive understanding of the process, we consider a problem in which a control plan involving multiple treatment variables is conducted in order to bring a response variable close to a target value with variation reduction. Using statistical causal analysis with linear (recursive and non-recursive) structural equation models, we configure an optimal control plan involving multiple treatment variables through causal parameters. Based on the formulation, we clarify the causal mechanism for how the variance of a response variable changes when the control plan is conducted. The results enable us to evaluate the effect of a control plan on the variance of a response variable from non-experimental data and provide a new application of linear structural equation models to engineering science.

Keywords:

• causal effects
• causal diagram
• confounding bias
• total effect
• variation reduction

Acknowledgements

We thank anonymous referees whose comments significantly improved the presentation of this paper. This paper was partially supported by the Ministry of Education, Culture, Sports, Science and Technology of Japan and the Asahi Glass Foundation.