A Study on the Reliability of Consecutive k-Out-of-n: G Systems Based on Copula

Abstract

The computation of reliability characteristics of a system that consists of dependent components is sometimes difficult especially when the type of dependence is not known. This article introduces the copula method to calculate the reliability of dependent consecutive k-out-of-n: G systems. The components in these systems are dependent on each other and the dependency may be either linear or nonlinear. The copula is a popular tool for modeling the dependence structure of data. It contains the information about the dependency structure of a vector of random variables and can capture nonlinear dependence. Based on the copula theory, the article analyzes the consecutive k-out-of-n: G systems and gets the reliability indexes. Finally, some numerical examples are presented to illustrate the results obtained in this article.

Keywords:

• Copula
• Consecutive k-out-of-n: Dependent failure
• G system
• Reliability

Mathematics Subject Classification:

• 62xx
• 62N05

Acknowledgment

This research is supported by the 211 project of Minzu University of China, the economic and social development in ethnic: minority areas analysis and prediction in China (021211030312).