
We use real-world data from a highly automated production line. Each unit travels along a conveyor
belt and passes through several process cells \(C_1,\ldots,C_6\) (see
Figure~\ref{fig:real_data_comparison}). In each cell, various automated manufacturing processes—such
as staking, welding, etc.—are performed. For example, cell \(C_1\) executes ten distinct tasks,
whereas cell \(C_4\) performs only two. For every process, a set of physical measurements is
extracted and recorded, denoted by \(\mathbf{X}_i\) for cell \(C_i\).
Their dimensionality range from one to \(13\).
In a staking process, for
instance, measurements like the press-in force and the maximum attained force are obtained to ensure
production quality. These individual process measurements form the causal groups of interest. We observe \(19\) groups, which together comprise \(121\) features. The full dataset contains approximately \(35,000\) parts, of which we randomly sample \(5,000\) for computational tractability.
\begin{figure}%[H]
  \centering
  \scalebox{0.6}{
    \input{./Figures/real_data_gresit.tex}
  }
  \caption{Learned causal edges from the real-world dataset using \textit{GRESIT-MURGS}}.
  \label{fig:real_data_comparison}
\end{figure}
Access to complete causal ground truth in real-world applications is typically prohibitive or unattainable~\citep{Goebler2024}. However, in production lines, partial causal ordering is available through domain knowledge due to the sequential nature of unit flow: processes in cell \(C_i\) can affect only those in cell \(C_j\) with \(i \le j\). Thus, we can partially assess learned graphs by their edge orientation.

Figure~\ref{fig:real_data_comparison} shows edges learned by \textit{GRESIT-MURGS}. Notably, only one edge conflicts with the cell-implied partial order. Conversely, \textit{GPC} yields many undirected edges and two directed edges, one violating the cell arrangement, while \textit{GGraN-DAG} identifies just two edges in cell \(C_3\). Lastly, applying \textit{GroupDirectLiNGAM}\citet{Entner2012} with MURGS pruning (Section\ref{sec:algorithms}) results exclusively in edges violating the partial ordering (see Section~\ref{sec:additional_results}). Thus, \textit{GRESIT-MURGS} produces the most meaningful causal structure in this setting.
