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Mixed-Effect Models for the Analysis and Optimization of Sheet-Metal Assembly Processes


Ivan Tomasic, Alf Andersson , Peter Funk

Publication Type:

Journal article


IEEE Transactions on Industrial Informatics




Assembly processes can be affected by various parameters, which is revealed by the measured geometrical characteristics (GCs) of the assembled parts deviating from the nominal values. Here, we propose a mixed-effect model (MEM) application for the purposes of analyzing variations in assembly cells, as well as for screening the input variables and characterization. MEMs make it possible to take into account statistical dependencies that originate from repeated measurements on the same assembly. The desirability functions approach was used to describe how to find corrective or control actions based on the fitted MEM. Objectives: To examine the usefulness of the MEM between the positions of the in-going parts as the input controllable variables and the measured GCs as the outputs. Methods: The data from 34 car frontal cross members (each measured three times) were experimentally collected in a laboratory environment by intentionally changing the positions of the in-going parts, assembling the parts, and subsequently measuring their GCs. A single MEM that completely describes the assembly process was fitted between the GCs and the positions of the in-going parts. Results: We present a modeling technique that can be used to establish which measured GCs are influenced by which controllable variables, and how this occurs. The fitted MEM shows evidence that the variability of some GCs changes over time. The natural variation in the system (i.e., unmodeled variations) is about two times larger than the variation between the assembled cross members. We also present two cases that demonstrate how to use the fitted MEM desirability functions to find corrective or control actions. Conclusion: MEMs are very useful tools for analyzing the assembly processes for car-body parts, which are nonlinear processes with multiple inputs and multiple correlated outputs. MEMs can potentially be applied in numerous industrial processes, since modern manufacturing plants measure all important process variables, which is the sole prerequisite for MEMs applications.


author = {Ivan Tomasic and Alf Andersson and Peter Funk},
title = {Mixed-Effect Models for the Analysis and Optimization of Sheet-Metal Assembly Processes},
volume = {15},
number = {2},
pages = {2194--2202},
month = {February},
year = {2017},
journal = {IEEE Transactions on Industrial Informatics },
url = {}