This repository contains a course project for Quality and Reliability Engineering that implements a multivariate statistical process control (MSPC) pipeline for monitoring high-dimensional, correlated process data.
Although developed in an academic setting, the project is structured to reflect real-world quality and reliability engineering practices, including robust baseline estimation and multivariate process monitoring.
- Course: Quality and Reliability Engineering
- Project Type: Applied statistical analysis
- Focus: Multivariate process monitoring and anomaly detection
The objective was to design and implement a statistically sound approach for detecting abnormal process behavior in systems where quality depends on many interrelated variables.
In modern operational systems (manufacturing, energy, healthcare operations), quality issues are expensive when detected late.
Traditional univariate control charts monitor variables independently and fail to capture multivariate interactions, leading to delayed detection of process drift, increased scrap, rework, and operational risk.
This project addresses that gap by developing a multivariate monitoring framework that establishes a clean in-control baseline and detects deviations early.
The notebook implements an end-to-end MSPC workflow:
- Exploratory Data Analysis
- Assess distributions and potential anomalies
- Standardization
- Ensure scale-invariant analysis
- Dimensionality Reduction (PCA)
- Address multicollinearity and stabilize covariance estimation
- Phase I: In-Control (IC) Identification
- Robust outlier detection using Elliptic Envelope
- Validation via Mahalanobis distance with chi-square thresholds
- Parameter Estimation
- Estimate mean vector and covariance matrix using IC data only
- Phase II: Monitoring
- Apply Hotelling’s T² control chart
- Identify out-of-control observations using statistical control limits
- PCA before monitoring to handle correlated, high-dimensional variables
- Robust Phase I cleaning to avoid biased control limits
- Hotelling’s T² for multivariate monitoring
- F-distribution–based control limits for statistical validity
All design choices are documented directly in the notebook using Markdown explanations.
The notebook produces:
- PCA scree and score plots
- Phase I IC vs OOC classification
- Hotelling’s T² control chart for Phase II monitoring
These outputs support both anomaly detection and process understanding.
- Python
- NumPy, Pandas, SciPy
- scikit-learn
- Matplotlib
The dataset used in this project is not included.
The analysis is dataset-agnostic and can be applied to any multivariate process data where rows represent observations and columns represent quality variables or sensor measurements.
This project demonstrates:
- Application of statistical quality control theory to realistic data
- Thoughtful methodological design, not black-box modeling
- Ability to reason about contamination, stability, and monitoring
- Clear communication of engineering decisions
- Root-cause contribution analysis
- Adaptive control limits
- Real-time or streaming process monitoring
- Integration with dashboards or APIs
Akshay Patel
Graduate Student – Industrial Engineering
- Clone the repository
git clone https://github.com/aksh-ay06/Quality-and-Reliability-Engineering-Final-Project cd /Quality-and-Reliability-Engineering-Final-Project