Soft Computing

, Volume 22, Issue 16, pp 5561–5568 | Cite as

An optimal model using data envelopment analysis for uncertainty metrics in reliability

  • Tianpei Zu
  • Rui Kang
  • Meilin WenEmail author
  • Yi Yang


Various uncertainty metrics have been applicable to measure reliability under aleatory uncertainty and epistemic uncertainty, including evidence-theory-based reliability, interval-analysis-based reliability, fuzzy-interval-analysis-based reliability, posbist reliability and belief reliability. Difficulties arise, however, when an attempt is made to solve one specific situation by implementing one of these methods since the evaluating results may be different from each other. It is unconvinced to choose one method merely based on the qualitative analysis. Therefore, this paper proposes an optimal evaluation model to conduct an objective evaluation on these metrics and provide reasonable decision-making proposals. An evaluating index system is established on the feature analysis of these metrics. Cooke classical model has been adopted to weigh experts’ performance and improve the objectivity of the quantification results. Considering both evaluation indexes and requirements from the demanding sides, an optimal model is introduced based on data envelopment analysis. Numerical examples are subsequently conducted to illustrate the evaluating methods. The proposed model was found to outperform alternative methods in terms of objectivity and ability to provide reasonable decision-making suggestions.


Optimal evaluating model Data envelopment analysis Uncertainty metrics Adaptabilities Capabilities 



This work was supported by the National Natural Science Foundation of China (Nos. 61573043, 71671009 and 61573041).

Compliance with Ethical Standards

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this paper.

Ethical Approval

This article does not contain any studies with human participants performed by any of the authors.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Reliability and Systems EngineeringBeihang UniversityBeijingChina
  2. 2.Department of Electrical and Computer EngineeringUniversity of British ColumbiaVancouverCanada

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