This project is part of the Quality Data Analysis course at Politecnico di Milano. The primary objective is to design and evaluate statistical methods for detecting defects in 3D-printed Voronoi filters. The study focuses on quality control through image analysis in a simulated production process.

The dataset was collected using a mock Flexible Manufacturing System (FMS) setup at the MADE Competence Center I4.0 laboratory. The system consisted of trays carrying parts along a rail. When positioned under a camera, the system captured an image of the tray. The setup is depicted in the figure below:

Each tray contains four parts, positioned in the four corners. The images captured represent defect-free parts, as shown below:

In the second phase, images of parts with defects were introduced into the dataset. An example of such defects is highlighted below:

The primary goal is to implement Statistical Process Control (SPC) charts to monitor quality and identify anomalies in real-time.

• Data from defect-free parts was restructured, analyzed, and modeled.
• Principal Component Analysis (PCA) was applied to reduce noise and highlight patterns in the data.
• Individual and multivariate SPC control charts were developed.

• Newly acquired data was modeled in the same way as Phase 1 data.
• Control charts developed in Phase 1 were applied to a dataset containing faulty parts.
• Faulty parts were identified based on control limits derived from the SPC charts.

• ARIMA modeling to address observed correlations.
• Seasonal ARIMA modeling to address periodicity observed in specific variables.

• Individual-Moving Range (I-MR) charts for monitoring PCA scores.
• Hotelling's T² control chart for multivariate analysis of original data and PCA scores.

• Control charts successfully identified faulty parts in the Phase 2 dataset.
• Hotelling's T² control charts built on non-transformed variables provided the best results.

The project consists of the following main files and folders:

• CSV.ipynb: The main analysis file written as a Jupyter Notebook.
• image_analysis_function.py: A Python function provided by the Department of Mechanical Engineering to transform images into CSV datasets containing numerical and characteristic information about part parameters.
• qda.py: A set of useful functions for Statistical Process Control (SPC), provided by the Department of Mechanical Engineering.
• Figs/: A folder containing figures used in the analysis report and README.
• dataset_phase1/: A folder containing data for Phase 1. It contains waw images collected during Phase 1 and a folder Result with the processed data from Phase 1. Inside this folder there is also a file image_statistics.csv - CSV file containing the the results of image analysis function for Phase 1 data.
• dataset_phase2/: A folder containing data for Phase 2. It contains waw images collected during Phase 2 and a folder Result_phase2 with the processed data from Phase 2. Inside this folder there is also a file image_statistics_phase2.csv - CSV file containing the the results of image analysis function for Phase 2 data.

The project consists of the following main files and folders:

• CSV.ipynb: The main analysis file written as a Jupyter Notebook.
• image_analysis_function.py: A Python function provided by the Department of Mechanical Engineering to transform images into CSV datasets containing numerical and characteristic information about part parameters. Provided by the Department of Mechanical Engineering, Politecnico di Milano.
• qda.py: A set of useful functions for Statistical Process Control (SPC), provided by the Department of Mechanical Engineering, Politecnico di Milano.
• Figs/: A folder containing figures used in the analysis report and README.
• dataset_phase1/: A folder containing data for Phase 1.
  • pictures: Raw images collected during Phase 1.
  • Result/: A folder containing processed data from Phase 1.
  • image_statistics.csv: CSV file containing the results of the image analysis function for Phase 1 data.
• dataset_phase2/: A folder containing data for Phase 2.
  • pictures: Raw images collected during Phase 2.
  • Result_phase2/: A folder containing processed data from Phase 2.
  • image_statistics_phase2.csv: CSV file containing the results of the image analysis function for Phase 2 data.

• The raw images of trays were processed using image_analysis_function.py. This script transformed the images into CSV datasets containing numerical and characteristic information about part parameters (e.g., area, perimeter, voids, etc.).
• Separate datasets were created for Phase 1 (defect-free parts) and Phase 2 (parts with faults):
  • Phase 1 Data: dataset_phase1/Results contains the processed images and the processed CSV file (image_statistics.csv).
  • Phase 2 Data: dataset_phase2/Results_Phase2 contains the processed images and the processed CSV file (image_statistics_phase2.csv). Acquisition of this data took place after Phase 1 was over.

• From the raw data, cumulative parameters were calculated to simplify and standardize the dataset. These included:
  • Total Area of Voids
  • Base Perimeter (Total Perimeter minus Void Perimeter)
  • Voids Perimeter
  • Number of Voids

• Defect-Free Data: Data from defect-free parts was used to establish baseline control charts.
• ARIMA Modeling: ARIMA models were applied to variables (e.g., void perimeter, base perimeter) to address any observed autocorrelations and in the data.
• Seasonal Adjustments: Seasonal ARIMA models were used to capture periodic behavior introduced by the physical layout of the trays (e.g., the position of parts affecting angular resolution).

• PCA was performed to reduce noise and highlight patterns in the data.
• The first three principal components were selected, capturing 95% of the variance in the dataset.
• PCA scores were used as inputs for control charts.

• Individual-Moving Range (I-MR) Charts: Used to monitor the individual PCA scores for anomalies.
• Hotelling's T² Control Chart: Applied to both original variables and PCA scores for multivariate analysis.
• Control limits were calculated to establish the baseline for detecting faulty parts.

• The datasets from Phase 2 were modeled using the same preprocessing steps as in Phase 1.
• The control charts developed in Phase 1 were applied to the new data.

• Faulty parts were identified by monitoring PCA scores and original variables against the control limits.
• Out-of-control points were flagged as anomalies, indicating potentially faulty parts.

• The control chart results were validated against a manually created list of known faulty parts.
• Performance Metrics: Confusion matrices were evaluated to assess the charts' effectiveness.

• Hotelling's T² control charts based on non-transformed variables provided the best results.

This project is licensed under the MIT License. See the LICENSE file for details.