A Reliability Test of a Complex System Based on Empirical Likelihood

Yan Zhou; Liya Fu; Jun Zhang; Yongchang Hui

doi:10.1371/journal.pone.0163557

A Reliability Test of a Complex System Based on Empirical Likelihood

PLoS One. 2016 Oct 19;11(10):e0163557. doi: 10.1371/journal.pone.0163557. eCollection 2016.

Authors

Yan Zhou¹, Liya Fu², Jun Zhang³, Yongchang Hui²

Affiliations

¹ College of Mathematics and Statistics, Institute of Statistical Sciences, Shenzhen University, Shenzhen, China.
² School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, China.
³ College of Mathematics and Computational Science, Institute of Statistical Sciences, Shen Zhen-Hong Kong Joint Research Center for Applied Statistical Sciences, Shenzhen University, Shenzhen, China.

Abstract

To analyze the reliability of a complex system described by minimal paths, an empirical likelihood method is proposed to solve the reliability test problem when the subsystem distributions are unknown. Furthermore, we provide a reliability test statistic of the complex system and extract the limit distribution of the test statistic. Therefore, we can obtain the confidence interval for reliability and make statistical inferences. The simulation studies also demonstrate the theorem results.

MeSH terms

Likelihood Functions
Monte Carlo Method
Reproducibility of Results
Statistics as Topic / methods*

Grants and funding

Y. Zhou’s research was supported by the Tianyuan Fund for Mathematics (No. 11526143), the Doctor Start Fund of Guangdong Province (No. 85118-000043) and The Natural Science Foundation of SZU (No. 836-00008303). L. Fu’s research was supported by The National Science Foundation of China (No. 11201365 and No. 11301408) and the Doctoral Programs Foundation of Ministry of Education of China (No. 2012020112005). Yongchang Hui’s research was supported by The National Science Foundation of China (No. 11401461). This study was also supported in part by Fundamental Research Funds for the Central Universities (No. 2015gjhz15). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.