MECH 580 A02: Design of Experiments for Hypothesis Testing and Modelling

Graduate-level course focusing on experimental design, statistical analysis, hypothesis testing, and uncertainty quantification for engineering research and applications.

Course Description PDF

Course Description

This graduate course provides students with advanced knowledge and practical skills in designing experiments for engineering research. The course covers statistical methods for hypothesis testing, experimental design methodologies, uncertainty analysis, and model development from experimental data.

Students learn to apply rigorous experimental design principles to optimize data collection, analyze experimental results with appropriate statistical tools, and develop predictive models based on experimental observations.

Instructor: Prof. Caterina Valeo

Course Objectives

The course aims to:

1. Develop expertise in planning and designing experiments for engineering research and industrial applications
2. Apply statistical methods for hypothesis testing and significance analysis
3. Understand and quantify measurement uncertainty and error propagation
4. Design experiments to optimize information gain while minimizing resource requirements
5. Build empirical and statistical models from experimental data
6. Critically evaluate experimental results and draw valid conclusions

Learning Outcomes

Upon successful completion, students will be able to:

1. Experimental Design: Design efficient experiments using factorial designs, response surface methodology, and optimization techniques
2. Statistical Analysis: Apply appropriate statistical tests for hypothesis testing, including t-tests, ANOVA, and regression analysis
3. Uncertainty Quantification: Conduct comprehensive uncertainty analysis including systematic and random errors, error propagation, and confidence intervals
4. Data Analysis: Analyze experimental data using modern statistical software and interpret results in engineering context
5. Model Development: Develop empirical models from experimental data and validate model predictions
6. Research Skills: Plan research experiments that generate publishable results with statistical rigor

Course Topics

Experimental Design Fundamentals

• Principles of experimental design
• Randomization, replication, and blocking
• Factorial designs and fractional factorial designs
• Response surface methodology
• Design of Experiments (DOE) for optimization

Statistical Methods

• Hypothesis testing and significance levels
• Confidence intervals and uncertainty bounds
• Analysis of Variance (ANOVA)
• Regression analysis and correlation
• Non-parametric statistical methods
• Model selection and validation

Uncertainty Analysis

• Types of measurement uncertainty
• Systematic vs. random errors
• Error propagation methods
• Uncertainty budgets
• Reporting experimental results with uncertainty

Advanced Topics

• Multi-objective optimization in experimental design
• Sequential experimental design
• Taguchi methods for robust design
• Monte Carlo simulation for uncertainty propagation
• Bayesian approaches to experimental design

Assessment

Assessment methods typically include:

• Assignments: Problem sets applying experimental design and statistical analysis methods
• Project: Design and analysis of a complete experiment relevant to student’s research
• Presentations: Communication of experimental results and statistical findings
• Examinations: Tests on theoretical concepts and practical applications

Target Audience

This course is designed for:

• Graduate students (Master’s and PhD) in Mechanical Engineering
• Students conducting experimental research in their thesis work
• Engineers requiring advanced skills in experimental design and data analysis
• Researchers seeking to improve the statistical rigor of their experimental work

Applications

Skills developed in this course are applicable to:

• Laboratory-based research in fluid mechanics, heat transfer, materials science, and vibrations
• Industrial experimentation and process optimization
• Quality control and Six Sigma methodologies
• Environmental monitoring and field measurements
• Design validation and verification testing
• Research and development in engineering companies

Software and Tools

Students will gain experience with:

• Statistical analysis software (e.g., R, MATLAB, Minitab)
• Design of Experiments software
• Data visualization tools
• Uncertainty analysis packages

Connection to Research

This course directly supports graduate research by providing:

• Statistical foundation for thesis experimental work
• Methods to design efficient experiments
• Tools for robust data analysis and interpretation
• Skills for publishing experimental results in peer-reviewed journals
• Understanding of reviewer expectations for experimental rigor

This special topics course is offered periodically based on student demand and instructor availability. Contact the instructor for information about future offerings.