Lectures on Component Reliability Analysis#
In 2025 there were 2 lectures on component reliability analysis, which are summarized below.
Lecture 1: Introduction to Component Reliability Analysis#
The main topics covered in this lecture were:
Refresher on MCS and illustrating that it is one of many ways to perform a component reliability analysis.
Noting that the key ingredients of MCS include a function
Review of the week 1 workshop assignment, and seeing how it can be reformulated as a limit-state function
Review of the 2 river discharge example and exploring the probability of various combinations of events (e.g., review and/or and introduce the more general “region of interest”)
Emphasize the importance of visualizing the probability density in a 2 variable case (e.g., contours of density and regions of interest)
Introduce the linearized function of random variables and connect it to similar concepts from MUDE (uncertainty propagation)
Explain that MCS is nice because it is easy to implement; other methods are challenging to implement but can be much more efficient
Define the 5 key ingredients of a component reliability analysis
Define the FORM algorithm
Lecture 2:#
Review the 5 key ingredients of a component reliability analysis
Review how to calculate probabilities with univariate distributions, including the standard normal distribution
Explain that the standard normal distribution can be calculated easily as a linear transformation of any random variable with the normal distribution
Illustrate the standard normal distribution with a 2D example, and how to visualize the probability density function
Illustrate the linearized limit state function and how it can be used to calculate the probability of failure
Define the multivariate standard normal distribution and illustrate rotational invariance; density is only a function of the distance from the origin
Confirm that simple linear algebra relationships can be used to evaluate the probability of failure, once the algorithm finds the design point.
Define and explain the three key parts of a FORM solution: the design point, \(x_i\), the reliability index, \(\beta\), and the importance factors, \(\alpha_i\).