What You Will Learn:

• Probability rules and conditional probabilities
• Expectation and variance of continuous functions and their manipulation
• Failure rate modeling
• Normal, lognormal, exponential, Weibull, binomial and Poisson distributions
• Reliability, mean time to failure and availability
• Data fitting and reliability estimation
• Multimodal distributions and mixed multiple failure mechanisms
• Reliability block diagrams
• Monte Carlo simulation
• Load-strength interference and probabilistic design
• First-order reliability methods
• Accelerated tests and acceleration factors
• Time to failure modeling for selected failure mechanisms in mechanical and electronic systems

Week 1:

• Introduction and Overview
• Rules of Probability

Week 2:

• Probability Examples
• Conditional Probability

Week 3:

• Expectations and Variance Definition
• Expectation and Variance of Continuous Functions
• Normal Distribution PDF and CDF

Week 4:

• Load-Strength Interference Theory
• Load-Strength Interference Examples

Week 5:

• Material Degradation and Time to Failure Modeling
• Practice Problems for Test 1

Week 6:

• Lognormal Distribution, Reliability, Hazard Rate and MTTF
• Test 1

Week 7:

• Exponential Distribution and Examples of MTTF Estimation
• Weibull Distribution

Week 8:

• Multimodal Distributions and Mixed Multiple Failure Mechanisms
• Goodness of Fit

Week 9:

• Binomial and Poisson Distributions
• Practice Problems for Test 2

Week 10:

• Reliability Block Diagrams
• Test 2

Week 11:

• Monte Carlo Simulation
• Uncertainty in Geometry, Load and Strength
• Covariance and Correlation

Week 12:

• Covariance and Correlation Examples
• First Order Reliability Methods Introduction

Week 13:

• First Order Reliability Methods Examples
• Reliability Review During Design

Week 14:

• Accelerated Degradation
• Accelerated Testing and Acceleration Factors
• Practice Problems for Test 3

Week 15:

• Time to Failure Models for Mechanical Systems
• Test 3