Lectures on Component Reliability Analysis

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, \(\alpha_i\).