# Fibers of Failure: Classifying Errors in Predictive Processes
## Abbreviations  
The following abbreviations are used in this manuscript:  
SHAP Shapley Additive Explanations  
AHCL Agglomerative Hierarchical Clustering  
PCA Principal Component Analysis  
ANN Artificial Neural Network  
CNN Convolutional Neural Network  
EAF Electric Arc Furnace  
EE Electrical Energy  
FiFa Fibres of Failure  
KS Kolmogorov-Smirnov  
LR Logistic Regression  
TDA Topological Data Analysis  
CDF Cumulative Distribution Function  
\begin{table}
\begin{tabular}{l l l c c} \hline \hline
**Parameter(s)** & **Description** & **Unit** & **Count** & **ANN/FiFa** \\ \hline \multirow{2}{*}{Electrical energy} & The electrical energy consumption logged in the & kWh & 1 & -/- \\  & transformer system & & & \\ \hline \multirow{2}{*}{Error} & The error from the ANN model predicting the electrical & \multirow{2}{*}{kWh} & 1 & -/- \\  & energy consumption & & & \\ \hline \multirow{2}{*}{Pre-heater energy} & The calculated energy provided to the scrap by the scrap & \multirow{2}{*}{kWh} & 1 & -/x \\  & pre-heater & & & \\ \hline \multirow{2}{*}{Other energy variables} & Related to the proprietary energy model used to & \multirow{2}{*}{kWh} & 12 & -/- \\  & determine when the molten steel is ready for tapping. & & & \\ \hline \multirow{2}{*}{Total Weight} & Total input weight of charged material & kg & 1 & x/x \\ \hline \multirow{2}{*}{Total Weight} & Total input weight of metallic material & kg & 1 & -/x \\ \hline \multirow{2}{*}{Slag Weight} & Total input weight of oxide material & kg & 1 & -/x \\ \hline \multirow{2}{*}{Oxide composition} & Weight percent of 11 oxides and 1 flouride & wt\% & 12 & -/x \\ \hline \multirow{2}{*}{Metal composition} & Weight percent of 26 alloying elements & wt\% & 26 & -/x \\ \hline \multirow{2}{*}{Additive Propane} & Total input of propane & \(m^{3}\) & 1 & x/x \\ \hline \multirow{2}{*}{Additive O2} & Total input of oxygen gas through lance & \(m^{3}\) & 1 & x/x \\ \hline \multirow{2}{*}{Additive O2 Burner} & Total input of oxygen gas through burner & \(m^{3}\) & 1 & x/x \\ \hline \multirow{2}{*}{Additive N2} & Total input of nitrogen gas through lance & \(m^{3}\) & 1 & -/x \\ \hline \multirow{2}{*}{Rawtypes} & Total input weight of each raw material category & kg & 7 & x/x \\ \hline \multirow{2}{*}{Process Time} & Defined as start of the heat to the end of the heat & min & 1 & x/x \\ \hline \multirow{2}{*}{Tap-To-Tap Time} & Defined in the proprietary logging system & min & 1 & x/x \\ \hline \multirow{2}{*}{Power-on Time} & Defined as the total time the electrical energy source is & \multirow{2}{*}{s} & \multirow{2}{*}{1} & -/- \\  & powered on & & & \\ \hline \multirow{2}{*}{Power-off Time} & Defined as the total time the electrical energy source is & \multirow{2}{*}{s} & \multirow{2}{*}{1} & -/- \\  & powered off & & & \\ \hline \multirow{2}{*}{First to last power-on} & Time between first to last power on of the electrical & \multirow{2}{*}{min} & \multirow{2}{*}{1} & -/x \\  & energy source & & & \\ \hline Charging Time & Total time spent charging scrap into the furnace & min & 1 & -/x \\ \hline Melting Remelting Time & Total time in melting and remelting stages of the process & min & 1 & -/x \\ \hline Melting Time & Total time in the melting stage of the process & min & 1 & -/x \\ \hline Refining Time & Total time in the refining stage of the process & min & 1 & -/x \\ \hline Tapping Time & Total time spent in the tapping stage & min & 1 & -/x \\ \hline \hline \end{tabular}
\end{table}
Table 4: All variables used in the EAF case. The “Count” column shows the number of variables representing the parameter. The ANN/FiFa column indicates whether the variables were used as input variables in their respective models: “x” indicates the variable(s) is part of the model while “-” indicates the variable is absent. Completely absent variables in both ANN and FiFa were still part of the qualitative analysis using the KS-statistic to identify groups in the Mapper graph.