Identifying Process Dynamics through a Two-Level Factorial Experiment

ABSTRACT

Dynamic processes undergo a transition time when changing experimental factors and therefore an experimenter is often interested in estimating effect dynamics alongside effect sizes. This article illustrates an eight-step analysis procedure for model identification of a multiple-input transfer function–noise model for the response from a two-level factorial experiment in a blast furnace process. Because real data often are affected by disturbances and missing observations, our proposed procedure deals with these problems and results in a transfer function–noise model that captures system dynamics and provides effect estimates from the experiment.

KEYWORDS:

• blast furnace experiments
• missing observations
• time series analysis
• transfer function–noise model
• transition time
• two-level factorial design

ACKNOWLEDGMENTS

The authors thank Swedish Steel AB, BDX, and the engineers at the blast furnace process for the contributions to the results presented here. Special thanks to Per Lagerwall at Swedish Steel AB and Håkan Johansson at BDX for their valuable contribution. The authors sincerely thank Dr. Murat Kulahci for valuable feedback on the work presented in this article. We thank two anonymous reviewers for valuable comments that significantly improved this article.

Notes

df=degrees of freedom; SD=standard deviation of the residuals; MAE=mean absolute prediction error.

The p -values for the estimated parameters are given above or below the parameter values. The arrows next to the model criteria indicate whether the corresponding criterion should be large ( ↑) or small ( ↓). All models are fitted using statistical software package SAS JMP 10.0. (SAS Institute Inc., Cary, NC).

df=degrees of freedom; SD=standard deviation of the residuals; MAE=mean absolute prediction error. The p-values for the estimated parameters are given above or below the parameter values. The arrows next to the model criteria indicate if the corresponding criterion should be large ( ↑) or small ( ↓). All models are fitted using statistical software package SAS JMP 10.0 (SAS Institute Inc., Cary, NC).