01 | Module
Why Deterministic Design Is Not Enough
Nominal values, safety factors, variability, reliability, robustness, and risk.
Start module ->Course 27 | Advanced Engineering Methods
Probabilistic Design and Reliability
Quantify variability, estimate failure probability, evaluate component and system reliability, and make robust or reliability-based design decisions.
Course snapshot
- Purpose
- Probabilistic Design and Reliability teaches engineers to quantify the effects of variability, estimate failure probability, evaluate component and system reliability, and make robust or reliability-based design decisions.
- Before this
- Related advanced courses
- Used in Career directions
- Content status
- Lesson hub
How to study this course
- Define the failure mode before choosing distributions
- Build a checkable mechanical model
- Represent uncertainty with evidence and units
- Estimate reliability analytically or by simulation
- Check convergence, sensitivity, and assumptions
- Recommend a design with residual risk stated clearly
01
What this course teaches
Variability becomes engineering evidence
The course moves from nominal safety factors to probability models, limit states, and failure probability, always tied to mechanical examples.
Computation is checked, not worshipped
Python labs use fixed seeds, units, analytical benchmarks, convergence checks, and interpretation so code supports judgement rather than replacing it.
Reliability is separated from VVUQ
VVUQ asks whether a model is credible for use. This course asks how uncertain inputs affect performance, failure, robustness, and design choice.
02
Learning outcomes
- Explain why deterministic nominal values and safety factors do not fully describe reliability.
- Represent engineering variability with suitable random variables and distributions.
- Define performance functions, safe regions, failure regions, and failure probability.
- Calculate stress-strength and serviceability reliability for simple components.
- Implement Monte Carlo reliability simulations and check convergence.
- Evaluate series, parallel, and mixed mechanical system reliability with dependence awareness.
- Interpret lifetime reliability, hazard, Weibull, lognormal, exponential, and censored data.
- Compare deterministic, robust, and reliability-based design decisions.
- Produce a reproducible Python reliability analysis with assumptions and residual risk.
03
Workload and assessment
Workload
10 modules, about 30 to 45 focused study hours, with a Python activity in every module.
Assessment
13 assessment points: readiness check, module retrieval checks, mid-course synthesis, final capstone, and report rubric.
Capstone
A cantilever bracket reliability case study: define failure modes, model uncertainty, estimate failure probability, redesign, and report residual risk.
04
The 10 modules
02 | Module
Probability Models for Engineering Variables
Random variables, distributions, dependence, parameter estimation, and model choice.
Start module ->03 | Module
Performance Functions and Limit States
Resistance, load, stress-strength interference, safe regions, and failure regions.
Start module ->04 | Module
Monte Carlo Simulation for Reliability
Sampling, random seeds, failure counting, confidence intervals, convergence, and rare-event limits.
Start module ->05 | Module
Reliability of Mechanical Systems
Series systems, parallel systems, mixed systems, common cause, block diagrams, and fault trees.
Start module ->06 | Module
Lifetime Reliability and Failure Data
Reliability functions, hazard, exponential, Weibull, lognormal models, and censoring.
Start module ->07 | Module
Uncertainty Propagation and Sensitivity
Analytical propagation, sampling, output distributions, sensitivity, and correlation effects.
Start module ->08 | Module
Robust Design
Mean-variance trade-offs, tolerance design, robustness metrics, and manufacturability.
Start module ->09 | Module
Reliability-Based Design
Chance constraints, target reliability, reliability index, risk-informed design, and independent checks.
Start module ->10 | Module
Engineering Reliability Case Study and Capstone
A complete reproducible probabilistic design study for a cantilever bracket.
Start module ->05
Course evidence package
Worked examples
20 worked examples cover stress-strength interference, Monte Carlo reliability, systems, lifetime data, robust design, and reliability-based redesign.
Computational labs
10 Python activities use NumPy where useful and include assumptions, units, checks, interpretation, and limitations.
References
The course is grounded in Haldar and Mahadevan, Elsayed, NIST/SEMATECH, Le, and Der Kiureghian, with original MechCompass wording and examples.