Higher-order normal approximation approach for highly reliable system assessment

Zhaohui Li, Dan Yu, Jian Liu, Qingpei Hu

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


In this study, the issue of system reliability assessment (SRA) based on component failure data is considered. In industrial statistics, the delta method has become a popular approach for confidence interval approximation. However, for high reliability systems, usually the assessment is confronted with very limited component sample size, variant multi-parameter lifetime models, and complex system structure. Along with strict requirement on assessment accuracy and computational efficiency, existing approaches barely work under these circumstances. In this article, a normal approximation approach is proposed for determining the lower confidence limit of system reliability using components’ time-to-failure data. The polynomial adjustment method is adopted to construct higher-order approximate confidence limit. The main contribution of this work is constructing an integrated methodology for SRA. Specifically, a reliability-based Winterbottom-extended Cornish-Fisher (R-WCF) expansion method for log-location-scale family is elaborated. The proposed methodology exceeds the efficient limitation of Cramer Rao’s theory. Numerical studies are conducted to illustrate the effectiveness of the proposed approach, and results show that the R-WCF approach is more efficient than the delta method for highly reliable system assessment, especially with ultra-small sample size. Supplementary materials are available for this article. Go to the publisher’s online edition of IISE Transactions.

Original languageEnglish (US)
Pages (from-to)555-567
Number of pages13
JournalIISE Transactions
Issue number5
StatePublished - May 3 2020


  • System reliability assessment
  • Winterbottom-extended Cornish–Fisher expansion
  • highly reliable system
  • log-location-scale family
  • reliability-based expansion

ASJC Scopus subject areas

  • Industrial and Manufacturing Engineering


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