FOSM Analysis for Engineering Decisions

Engineering decisions are always made under some degree of uncertainty, from soil properties to structural loads. Understanding how these variations propagate through your design formulas is critical to ensuring safety and reliability. This course teaches you how to apply First-Order Second-Moment (FOSM) analysis to calculate uncertainty in systems with multiple variables. You will transition from deterministic calculations to probabilistic engineering, gaining the skills to quantify risk and predict performance variations in complex designs. What you'll learn: - Understand the core mathematical concepts of probability, variance, and covariance in engineering - Apply Taylor series expansions to approximate functions of many variables - Calculate mean and variance propagation through multi-variable engineering equations - Analyze foundation settlement scenarios to assess structural risk under soil uncertainty - Evaluate safety margins and probability of failure using calculated reliability indices - Integrate modern sensitivity analysis to identify which design variables impact performance the most This course begins with foundational definitions of uncertainty and probability before guiding you step-by-step through the mathematical derivations of FOSM. You will then study practical engineering scenarios, including a detailed look at foundation settlement calculations, to see how these methods apply to real-world infrastructure. This course is designed for engineering students, civil and environmental engineers, and project planners who want to move beyond simple safety factors. No prior background in advanced probability theory is required, though a basic understanding of calculus is helpful. Start mastering uncertainty analysis and design safer, more resilient engineering systems today.