A Mean Value Reliability Method for Bimodal Distributions


In traditional reliability problems, the distribution of a basic random variable is usually unimodal; in other words, the probability density of the basic random variable has only one peak. In real applications, some basic random variables may follow bimodal distributions with two peaks in their probability density. For example, the random load of a bridge may have two peaks, with a distribution consisting of a weighted sum of two normal distributions, suggested by traffic load data. When binomial variables are involved, traditional reliability methods, such as the First Order Second Moment (FOSM) method and the First Order Reliability Method (FORM), will not be accurate. This study investigates the accuracy of using the saddlepoint approximation for bimodal variables and then employs a mean value reliability method to accurately predict the reliability. A limit-state function is at first approximated with the first order Taylor expansion so that it becomes a linear combination of the basic random variables, some of which are bimodally distributed. The saddlepoint approximation is then applied to estimate the reliability. Examples show that the new method is more accurate than FOSM and FORM.

Meeting Name

ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2017 (2017: Aug. 6-9, Cleveland, OH)


Mechanical and Aerospace Engineering


This material is based upon work supported by the National Science Foundation under grant CMMI 1562593 and the Intelligence Systems Center at Missouri University of Science and Technology.

Keywords and Phrases

Computer Aided Design; Design; Normal Distribution; Probability Density Function; Random Variables; Reliability; Structural Analysis, Bimodal Distribution; First Order Reliability Methods; First Order Second Moment Method; Limit State Functions; Linear Combinations; Probability Densities; Reliability Problems; Saddle-Point Approximation, Probability Distributions

International Standard Book Number (ISBN)


Document Type

Article - Journal

Document Version


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© 2017 American Society of Mechanical Engineers (ASME), All rights reserved.

Publication Date

01 Aug 2017