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research-article

Reliability Methods for Bimodal Distribution with First Order Approximation

[+] Author and Article Information
Zhangli Hu

Department of Mechanical and Aerospace Engineering, Missouri University of Science and Technology, 258A Toomey Hall, 400 West 13th Street Rolla, MO 65409-0500
zh3zd@mst.edu

Xiaoping Du

Professor Department of Mechanical and Aerospace Engineering, Missouri University of Science and Technology, 272 Toomey Hall, 400 West 13th Street, Rolla, MO 65409-0500
dux@mst.edu

1Corresponding author.

ASME doi:10.1115/1.4040000 History: Received November 05, 2017; Revised April 15, 2018

Abstract

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. 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 saddlepoint approximation based reliability methods with first order approximation to 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 saddlepoint approximation based reliability methods are more accurate than FOSM and FORM.

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