Probability & Statistics

Semester-long graduation project:

 A semester-long graduation project aligned with the "Probability and Statistics" course for Engineering students helps them apply theory to real-world design. It reinforces cross-disciplinary thinking—critical in areas like engineering systems. These projects are designed to evolve in complexity over the semester, allowing students to apply theoretical knowledge to real-world problems, develop design and analysis skills, and encourage cross-disciplinary thinking.

🎓 Semester-Long Graduation Project Ideas (Probability & Statistics for Engineers)

🔧 1. Reliability Analysis of an Engineering System

Objective: Model and analyse the reliability of a multi-component system (e.g., electrical circuit, mechanical assembly, or software system).

Phases:

·        Identify components and failure modes.

·        Use probabilistic models (Exponential, Weibull) to simulate failure rates.

·        Use reliability block diagrams or fault trees.

·        Estimate mean time to failure (MTTF) and system availability.

·        Include real-world maintenance scenarios and optimize for reliability.

Disciplines: Mechanical, Electrical, Industrial, Systems Engineering

📈 2. Predictive Maintenance Using Statistical Modeling

Objective: Design a statistical system for predicting machine or equipment failure using historical data.

Phases:

·        Collect (or simulate) time-series maintenance data.

·        Apply Poisson or Exponential models for event (failure) occurrences.

·        Use control charts and hypothesis testing to detect anomalies.

·        Propose maintenance schedules based on predictive insights.

Disciplines: Mechanical, Mechatronics, Data Science, Industrial

🏭 3. Statistical Quality Control in Manufacturing

Objective: Design a quality control process for a simulated (or real) manufacturing line using statistical tools.

Phases:

·        Define critical quality parameters and specifications.

·        Collect data (real or synthetic) from a process.

·        Apply control charts (X-bar, R-chart), process capability indices (Cp, Cpk).

·        Simulate process improvements using Six Sigma principles.

·        Develop a quality reporting dashboard.

Disciplines: Manufacturing, Industrial, Mechanical

📊 4. Data-Driven Decision System for Traffic Management

Objective: Use probabilistic and statistical models to analyse and optimize traffic flow at a busy intersection or area.

Phases:

·        Collect/simulate traffic flow data.

·        Model arrival rates using the Poisson distribution.

·        Analyse waiting times and optimize signal timings using probability distributions.

·        Use simulation tools (e.g., Arena, MATLAB) for performance analysis.

·        Propose real-world improvements based on statistical findings.

Disciplines: Civil, Transportation, Systems Engineering

🌱 5. Environmental Risk Assessment using Monte Carlo Simulation

Objective: Assess environmental risk (e.g., pollution levels, flood probability) using Monte Carlo and probabilistic modelling.

Phases:

·        Define random variables (rainfall, contamination rate, etc.).

·        Develop probability distributions based on past data.

·        Run Monte Carlo simulations to estimate risk probabilities.

·        Analyse statistical confidence intervals and suggest risk mitigation strategies.

Disciplines: Environmental, Civil, Systems Engineering

⚙️ 6. Engineering Design Under Uncertainty

Objective: Redesign an existing product/component to account for variability in material properties, loading conditions, etc.

Phases:

·        Define design parameters and uncertainties.

·        Model uncertainties using probability distributions.

·        Perform statistical sensitivity analysis.

·        Apply safety factors using reliability theory.

·        Finalize robust design with statistical justification.

Disciplines: Mechanical, Civil, Aerospace, Materials

🧪 7. Experimental Data Analysis and Model Fitting

Objective: Experiment and use statistical inference to build and validate a model.

Phases:

·        Design an experiment (e.g., stress-strain test, heat dissipation, chemical yield).

·        Collect data and clean/analyze it.

·        Fit a probabilistic/statistical model (regression, exponential, normal, etc.).

·        Validate model assumptions and perform goodness-of-fit tests.

·        Use the model to make predictions and suggest optimizations.

Disciplines: Multidisciplinary – fits all engineering fields

🧠 8. Smart Sensor Data Analysis for Anomaly Detection

Objective: Build or simulate a smart sensor system (IoT) and develop a statistical model to detect abnormal behavior.

Phases:

·        Define system variables and generate or collect sensor data.

·        Apply moving averages, control limits, and Chebyshev’s inequality.

·        Detect outliers and statistically justify anomalies.

·        Build a simple dashboard or alert system based on statistical thresholds.

Disciplines: Electrical, Mechatronics, Computer, Data Engineering

🏗️ 9. Probabilistic Structural Load Analysis

Objective: Analyze the structural integrity of a simple structure (e.g., beam, truss) under probabilistic loading.

Phases:

·        Define random load and material properties.

·        Apply probabilistic models to estimate maximum load capacity.

·        Use Monte Carlo simulation or reliability indices.

·        Recommend design improvements for robustness.

Disciplines: Civil, Structural, Mechanical Engineering

🛰️ 10. Satellite Communication Reliability Modeling:

Objective: Analyze failure rates and data loss probabilities in a communication link (e.g., satellite or wireless system).

Phases:

·        Define failure events (e.g., signal loss, component failure).

·        Model time-to-failure using Exponential/Poisson distributions.

·        Calculate link availability, reliability, and expected downtime.

·        Design improvements and simulate better configurations.

Disciplines: Electrical, Communication, Aerospace Engineering

🧩 Optional Enhancements (for all projects)

·        Use statistical software: Python, MATLAB, R, or Excel

·        Data visualization: Build dashboards or reports

·        Real-world data: Use open datasets or collect new data

·        Documentation: Full engineering report with statistical justification, interpretation, and recommendations

📘 Structure for All Projects: 

To ensure students progress throughout the semester, projects can be divided into weekly or bi-weekly milestones, like: