Predicting Slow Mechanical Watch Movements using XGBoost: A Technical Approach

 Predicting Slow Mechanical Watch Movements using XGBoost: A Technical Approach

 Introduction

This article explores the use of XGBoost to predict why a mechanical watch movement might be running slow. The emphasis will be on how different classification metrics, such as Brier Score, Cohen's Kappa, and Precision-Recall AUC, can help tune model performance. One key aspect of the analysis is threshold tuning, which plays a crucial role in optimizing classification results for an imbalanced dataset.

 

 Understanding Mechanical Watch Performance

Mechanical watches rely on precise movements to keep accurate time. Over time, certain factors like lubrication, wear, or exposure to temperature fluctuations and magnetism can cause the watch to slow down. By collecting data on these factors, we can predict and diagnose potential issues before they significantly affect the watch's performance.

 

1. Amplitude: The angle of oscillation of the balance wheel.

2. Lubrication: Condition of oils within the movement.

3. Power Reserve: Remaining energy in the watch, affecting timekeeping.

 

 Why XGBoost for This Problem?

XGBoost is highly efficient, offering features like handling missing data, robust regularization, and parallel computation. It provides a suitable framework for classifying whether a watch is likely to run slow based on its movement data.

 

 The Importance of Thresholds in Classification

A critical element of classification problems is the threshold. By default, XGBoost assigns predictions based on a probability threshold of 0.5. However, this is often suboptimal, especially when dealing with imbalanced data, where one class (e.g., normal functioning watches) vastly outweighs the other (e.g., slow watches). Adjusting the classification threshold can significantly impact the balance between precision and recall.

 

For example, if the default threshold of 0.5 results in many false positives (normal watches incorrectly labeled as slow), lowering the threshold to 0.3 could yield better precision by focusing on more confident predictions.

 Key Metrics for Classification

1. Brier Score: Measures the accuracy of probabilistic predictions. A lower Brier score reflects better-calibrated probability estimates for watch slowdowns.

2. Cohen's Kappa: This metric adjusts for chance agreement, crucial when the dataset is imbalanced.

   This helps in tuning the model to minimize bias toward the more frequent class (normal function).

 

3. Precision-Recall AUC (PR-AUC): A measure better suited for imbalanced data, as it focuses on the trade-off between precision (low false positives) and recall (low false negatives).

 

4. F1 Score: Harmonic mean of precision and recall. It helps in balancing false positives and false negatives in prediction.

 

 Data Preprocessing and Feature Engineering

Data features include:

- Balance Wheel Amplitude

- Lubrication Condition

- Magnetism Exposure

- Power Reserve

- Temperature

 

These features influence the watch’s accuracy and performance, and XGBoost can rank their importance based on how they impact model outcomes.

 

 Model Development

 

1. Data Splitting: Using an 80/20 train-test split ensures that the model has enough data to generalize.

2. Cross-Validation: We apply stratified cross-validation to account for class imbalance, ensuring that each fold has an equal representation of normal and slow watches.

3. Threshold Tuning: Evaluate performance at various thresholds using precision, recall, and F1 score.

   - A lower threshold, say 0.3, could maximize recall, detecting more slow watches.

   - Alternatively, a higher threshold improves precision, but at the cost of missing slow cases.

 

 Results

Feature Importance provided by XGBoost shows the relative influence of factors such as Balance Wheel Amplitude and Lubrication Condition on the model's predictions.

 

By adjusting the threshold, the model can achieve a F1 Score that balances false negatives and positives. Cohen's Kappa is maximized to reduce the likelihood of random classification, and Brier Score helps in validating the reliability of predicted probabilities.

 

 Conclusion

By leveraging advanced evaluation metrics and threshold tuning, we can build a well-calibrated XGBoost model to predict slowdowns in mechanical watch movements. These insights provide valuable feedback for watch technicians to make informed maintenance decisions.

 

 References

- [XGBoost Documentation](https://xgboost.readthedocs.io/)