@article{lic-che-yix-tao-11-aa-reliab,
  author = {Li, Chun-yang and Chen, Xun and Yi, Xiao-shan and Tao, Jun-yong},
  title = {Interval-Valued Reliability Analysis of Multi-State Systems}, 
  journal = {IEEE Transactions on Reliability}, 
  year = 2011,
  volume = {60},
  number = {1},
  pages = {323-330},
  keywords = {},
  doi = {10.1109/TR.2010.2103670},
  issn = {1558-1721},
  month = mar,
  abstract = {In previous studies that analyzed the reliability of multi-state systems, the precise values of the state performance levels and state probabilities of multi-state components were required. In many cases, however, there are insufficient data to obtain the state probabilities of components precisely. A method is proposed in this paper to analyze the reliability of multi-state systems when the available data of components are insufficient. Based on the Bayesian approach and the imprecise Dirichlet model, the interval-valued state probabilities of components are obtained instead of precise values. The interval universal generating function is developed, and the corresponding operators are defined to estimate the interval-valued reliability of multi-state systems. Affine arithmetic is used to improve the interval-valued reliability. A numerical example illustrates the proposed method. The results show that the proposed method is efficient when state performance levels and/or state probabilities of components are uncertain and/or imprecise.}
}