Reliability index for non-normal distributions of limit state functions

Seyed Hooman Ghasemi, Andrzej S. Nowak

Research output: Contribution to journalArticlepeer-review

43 Scopus citations


Reliability analysis is a probabilistic approach to determine a safety level of a system. Reliability is defined as a probability of a system (or a structure, in structural engineering) to functionally perform under given conditions. In the 1960s, Basler defined the reliability index as a measure to elucidate the safety level of the system, which until today is a commonly used parameter. However, the reliability index has been formulated based on the pivotal assumption which assumed that the considered limit state function is normally distributed. Nevertheless, it is not guaranteed that the limit state function of systems follow as normal distributions; therefore, there is a need to define a new reliability index for no-normal distributions. The main contribution of this paper is to define a sophisticated reliability index for limit state functions which their distributions are non-normal. To do so, the new definition of reliability index is introduced for non-normal limit state functions according to the probability functions which are calculated based on the convolution theory. Eventually, as the state of the art, this paper introduces a simplified method to calculate the reliability index for non-normal distributions. The simplified method is developed to generate non-normal limit state in terms of normal distributions using series of Gaussian functions.

Original languageEnglish (US)
Pages (from-to)365-372
Number of pages8
JournalStructural Engineering and Mechanics
Issue number3
StatePublished - May 10 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering
  • Building and Construction
  • Mechanics of Materials
  • Mechanical Engineering


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