Yield Optimization

Idea

By removing anomalies and tightening control limits, aiming to reduce variability and improve yield.

1. Comparing ML Anomalies with Statistical Control Limits

• Scenario 1: If ML detects anomalies outside the initial control limits (mean ± 3σ), it confirms that the limits are reasonable.
• Scenario 2: If ML detects anomalies inside the initial control limits, it suggests that the statistical limits may need tightening.

Example:

• Initial control limit for Parameter1: (40, 60)
• ML detects anomalies within the range (45, 55).
• This implies that extreme values between 40–45 and 55–60 should also be treated as risky.
• Action: Adjust the control limits to a tighter range.

2. Data-Driven Control Limit Adjustment

• Recalculate boundaries using only non-anomalous data.
• Replace the traditional mean ± 3σ approach with a method based on "good data."

New Control Limit Calculation:

• Lower Control Limit (LCL):
  [ LCL_{new} = Q1 - 1.5 \times IQR ]
• Upper Control Limit (UCL):
  [ UCL_{new} = Q3 + 1.5 \times IQR ] where ( IQR ) (Interquartile Range) = ( Q3 - Q1 ).

3. Process Optimization Using Anomaly-Free Data

• Refined control limits ensure tunable parameters stay within optimized boundaries.
• This reduces process variations and improves yield.

4. Implementation in Code

• Recalculate control limits using only non-anomalous data.
• Optimize yield by recommending new parameter settings.

More Approach:

• Dynamic control limits for changing processes
• Advanced anomaly detection algorithms (e.g., DBSCAN, Autoencoders).
• Multivariate control limits to account for parameter correlations.
  • Instead of calculating control limits for each parameter independently, use multivariate techniques to account for correlations between parameters.
  • Example: Use Principal Component Analysis (PCA) to reduce dimensionality and detect anomalies in the transformed space.

  •  from sklearn.decomposition import PCA
     pca = PCA(n_components=2)
     transformed_data = pca.fit_transform(data.iloc[:, :-1])
     iso_forest = IsolationForest(contamination=0.05, random_state=42)
     data['PCA_Anomaly'] = iso_forest.fit_predict(transformed_data) == -1

• Bayesian optimization for direct yield maximization.
• Clustering-based control for pattern recognition.
• Use clustering algorithms (e.g., K-Means) to group data into clusters and identify clusters with poor yield.
• Define control limits based on the "good" clusters.

Which Method to Choose?

• If your process is stable: Your current method (statistical + Isolation Forest) is likely sufficient.
• If your process is dynamic: Consider dynamic control limits or Bayesian optimization.
• If parameters are correlated: Use multivariate techniques like PCA or clustering.
• If you want to explore alternatives: Try DBSCAN, One-Class SVM, or Autoencoders for anomaly detection.

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Note: The above steps provide a systematic approach to improve yield by leveraging ML-based anomaly detection and data-driven control limit adjustments.