Category: Reliability Analysis of Structures.

System Reliability

• In this lesson, we discuss an application of probability to predict an overall system’s reliability. • Reliability of a…

Advanced first-order second moment method (AFOSM)

Hasofer-Lind Reliability Index Hasofer and Lind proposed a modified reliability index that did not exhibit the invariance problem illustrated in…

First-order second moment method (FOSM)

This method is also referred to as mean value first-order second moment (MVFOSM) method, and it is based on the…

RELIABILITY INDEX

Reduced Variables It is convenient to convert all random variables to their “standard form;’ which is a non dimensional form…

Levels of reliability methods

There are different levels of reliability analysis, which can be used in any design methodology depending on the importance of…

Reliability Analysis

Reliability analysis refers to the fact that a scale should consistently reflect the construct it is measuring. There are certain times…

What is a Lognormal Distribution?

A lognormal (log-normal or Galton) distribution is a probability distribution with a normally distributed logarithm. A random variable is lognormally distributed if…

The Poisson Distribution and Poisson Process Explained

A tragedy of statistics in most schools is how dull it’s made. Teachers spend hours wading through derivations, equations, and…

Chebyshev’s Theorem

What is Chebyshev’s Theorem? Chebyshev’s theorem is used to find the proportion of observations you would expect to find within two standard deviations…

Mathematical Expectation

Properties and Assumptions:

Probability Density Function

Probability Mass Function

For discrete random variables, the PMF is also called the probability distribution. Thus, when asked to find the probability distribution of…