Journal of Mechanical Science and Technology

, Volume 32, Issue 11, pp 5111–5119 | Cite as

Characterizing wafer stage transmission errors via binary decision diagram and dynamic fault tree

  • Junyu Guo
  • Guo-Zhong Fu
  • Hong-Zhong Huang
  • Yu LiuEmail author
  • Yan-Feng Li


The wafer stage, as a key subsystem of the dual-stage lithographic tool, possesses the characteristic of high moving accuracy. The fault tree analysis (FTA), which plays an important role in the design stage of the wafer stage, is performed to distinguish the critical events leading to the overall transmission error. However, in view of the complexity of the wafer stage’s structure and operation mechanism, the binary decision diagrams and dynamic fault tree analysis methods are implemented in this paper to obtain a simplified calculation process and a supplement with the dynamic characteristic respectively. This is not achieved by the traditional FTA method. The event “wafer stage’s repetitive error along X axis exceeds 5 nm” is viewed as the top event of the fault tree. In this paper, we identify the critical factors affecting the kinematic accuracy of the wafer stage.


Wafer stage Kinematic accuracy Fault tree analysis Binary decision diagram Dynamic fault tree analysis 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    H. Levinson, Principles of lithography: Third edition, SPIE Press, Bellingham, USA (2010).Google Scholar
  2. [2]
    H. Z. Huang, X. Tong and M. J. Zuo, Posbist fault tree analysis of coherent systems, Reliability Engineering & System Safety, 84 (2) (2004) 141–148.CrossRefGoogle Scholar
  3. [3]
    B, Zheng, H. Z. Huang, W. Guo, Y. F. Li and J. Mi, Fault diagnosis method based on supervised particle swarm optimization classification algorithm, Intelligent Data Analysis, 22 (1) (2018) 191–210.CrossRefGoogle Scholar
  4. [4]
    H. A. Watson, Launch control safety study, Bell labs (1961).Google Scholar
  5. [5]
    J. Choi, K. Hwang and B. Kim, Reliability analysis for thermal cutting method based non–explosive separation device, Journal of Mechanical Science and Technology, 30 (12) (2016) 5433–5438.CrossRefGoogle Scholar
  6. [6]
    X. Y. Li, H. Z. Huang, Y. F. Li and E. Zio, Reliability assessment of multi–state phased mission system with nonrepairable multi–state components, Applied Mathematical Modelling, 61 (2018) 181–199.MathSciNetCrossRefGoogle Scholar
  7. [7]
    J. Jang, W. Kwon, S. Chun and Y. Moon, Reliability analysis of process–induced cracks in rotary swaged shell nose part, Journal of Mechanical Science and Technology, 26 (7) (2012) 2155–2158.CrossRefGoogle Scholar
  8. [8]
    J. L. Zhou and Q. Sun, Reliability analysis based on binary decision diagrams, Journal of Quality in Maintenance Engineering, 4 (2) (1998) 150–161.CrossRefGoogle Scholar
  9. [9]
    S. B. Akers, Binary decision diagrams, IEEE Transactions on Computers, 6 (1978) 509–516.CrossRefzbMATHGoogle Scholar
  10. [10]
    R. E. Bryant, Graph–based algorithms for boolean function manipulation, IEEE Transactions on Computers, 100 (8) (1986) 677–691.CrossRefzbMATHGoogle Scholar
  11. [11]
    J. Sadeghi and H. Askarinejad, Application of neural networks in evaluation of railway track quality condition, Journal of Mechanical Science and Technology, 26 (1) (2012) 113–122.CrossRefGoogle Scholar
  12. [12]
    H. Z. Huang, H. Zhang and Y. Li, A new ordering method of basic events in fault tree analysis, Quality and Reliability Engineering International, 28 (3) (2012) 297–305.CrossRefGoogle Scholar
  13. [13]
    J. B. Dugan, S. J. Bavuso and M. A. Boyd, Dynamic faulttree models for fault–tolerant computer systems, IEEE Transactions on Reliability, 41 (3) (1992) 363–377.CrossRefzbMATHGoogle Scholar
  14. [14]
    S. Montani, L. Portinale, A. Bobbio and D. Codetta–Raiteri, Radyban: A tool for reliability analysis of dynamic fault trees through conversion into dynamic Bayesian networks, Reliability Engineering & System Safety, 93 (7) (2008) 922–932.CrossRefGoogle Scholar
  15. [15]
    F. Chiacchio, L. Compagno, D. D'Urso, G. Mannoa and N. Trapani, Dynamic fault trees resolution: A conscious tradeoff between analytical and simulative approaches, Reliability Engineering & System Safety, 96 (11) (2011) 1515–1526.CrossRefGoogle Scholar
  16. [16]
    K. D. Rao, V. Gopika, V. V. S. S. Rao, H. S. Kushwaha, A. K. Vermab and A. Srividyab, Dynamic fault tree analysis using Monte Carlo simulation in probabilistic safety assessment, Reliability Engineering & System Safety, 94 (4) (2009) 872–883.CrossRefGoogle Scholar
  17. [17]
    D. Codetta–Raiteri, The conversion of dynamic fault trees to stochastic Petri nets, as a case of graph transformation, Electronic Notes in Theoretical Computer Science, 127 (2) (2005) 45–60.CrossRefzbMATHGoogle Scholar
  18. [18]
    J. Mi, Y. F. Li, W. Peng and H. Z. Huang, Reliability analysis of complex multi–state system with common cause failure based on evidential networks, Reliability Engineering & System Safety, 174 (2018) 71–81.CrossRefGoogle Scholar
  19. [19]
    H. Z. Huang, C. G. Huang, Z. Peng, Y. F. Li and H. Yin, Fatigue life prediction of fan blade using nominal stress method and cumulative fatigue damage theory, International Journal of Turbo & Jet Engines, Doi:–2017–0015.CrossRefGoogle Scholar
  20. [20]
    X. Y. Li, H. Z. Huang and Y. F. Li, Reliability analysis of phased mission system with non–exponential and partially repairable components, Reliability Engineering & System Safety, 175 (2018) 119–127.CrossRefGoogle Scholar
  21. [21]
    C. Ibáñez–Llano, A. Rauzy, E. Meléndez and F. Nieto, A reduction approach to improve the quantication of linked fault trees through binary decision diagrams, Reliability Engineering System Safety, 95 (12) (2010) 1314–1323.CrossRefGoogle Scholar

Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Junyu Guo
    • 1
    • 2
  • Guo-Zhong Fu
    • 2
  • Hong-Zhong Huang
    • 2
  • Yu Liu
    • 2
    Email author
  • Yan-Feng Li
    • 2
  1. 1.School of Mechanical and Electrical EngineeringUniversity of Electronic Science and Technology of ChinaChengdu, SichuanChina
  2. 2.Center for System Reliability and SafetyUniversity of Electronic Science and Technology of ChinaChengdu, SichuanChina

Personalised recommendations