Frontiers of Mechanical Engineering

, Volume 14, Issue 1, pp 21–32 | Cite as

Principle of maximum entropy for reliability analysis in the design of machine components

  • Yimin Zhang
Research Article
Part of the following topical collections:
  1. Innovative Design and Intelligent Design


We studied the reliability of machine components with parameters that follow an arbitrary statistical distribution using the principle of maximum entropy (PME). We used PME to select the statistical distribution that best fits the available information. We also established a probability density function (PDF) and a failure probability model for the parameters of mechanical components using the concept of entropy and the PME. We obtained the first four moments of the state function for reliability analysis and design. Furthermore, we attained an estimate of the PDF with the fewest human bias factors using the PME. This function was used to calculate the reliability of the machine components, including a connecting rod, a vehicle half-shaft, a front axle, a rear axle housing, and a leaf spring, which have parameters that typically follow a non-normal distribution. Simulations were conducted for comparison. This study provides a design methodology for the reliability of mechanical components for practical engineering projects.


machine components reliability arbitrary distribution parameter principle of maximum entropy 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



We would like to express our appreciation to the National Natural Science Foundation of China (Grant No. U1708254) for supporting this research.


  1. 1.
    Kapur K C, Lamberson L R. Reliability in Engineering Design. New York: John Wiley & Sons, 1977Google Scholar
  2. 2.
    Dhillon B S, Singh C. Engineering Reliability. New York: John Wiley & Sons, 1981zbMATHGoogle Scholar
  3. 3.
    Henley E J, Kumamoto H. Reliability Engineering and Risk Assessment. Englewood Cliffs: Prentice-Hall Inc., 1981Google Scholar
  4. 4.
    O’Connor P D T. Practical Reliability Engineering. New York: John Wiley & Sons, 1984Google Scholar
  5. 5.
    Wasserman G S. Reliability Verification, Testing, and Analysis in Engineering Design. New York: Marcel Dekker, Inc., 2002CrossRefGoogle Scholar
  6. 6.
    Ang A H S, Tang W H. Probability Concepts in Engineering Planning and Design. New York: John Wiley & Sons, 2006Google Scholar
  7. 7.
    Elsayed A E. Reliability Engineering. 2nd ed. New York: John Wiley & Sons, 2012zbMATHGoogle Scholar
  8. 8.
    Klyatis L M. Accelerated Reliability and Durability Testing Technology. New York: John Wiley & Sons, 2012zbMATHGoogle Scholar
  9. 9.
    Zhang Y. Reliability Design of Automobile Components. Beijing: Beijing Institute of Technology Press, 2000 (in Chinese)Google Scholar
  10. 10.
    Zhang Y. Introduction of Mechanical Reliability. Beijing: Science Press, 2012 (in Chinese)Google Scholar
  11. 11.
    Zhang Y. Reliability-based design for automobiles in China. Frontiers of Mechanical Engineering in China, 2008, 3(4): 369–376CrossRefGoogle Scholar
  12. 12.
    Zhang Y. Connotation and development of mechanical reliabilitybased design. Chinese Journal of Mechanical Engineering, 2010, 46 (14): 167–188CrossRefGoogle Scholar
  13. 13.
    Zhang Y. Review of theory and technology of mechanical reliability for dynamic and gradual systems. Journal of Mechanical Engineering, 2013, 49(20): 101–114 (in Chinese)CrossRefGoogle Scholar
  14. 14.
    Zhang Y, Sun Z. The reliability syllabus of mechanical products. Journal of Mechanical Engineering, 2014, 50(14): 14–20 (in Chinese)CrossRefGoogle Scholar
  15. 15.
    Siddall J N. Optimal Engineering Design: Principles and Application. New York: Marcel Dekker, 1982Google Scholar
  16. 16.
    Dai Y S, Xie M, Long Q, et al. Uncertainty analysis in software reliability modeling by Bayesian approach with maximum-entropy principle. IEEE Transactions on Software Engineering, 2007, 33 (11): 781–795CrossRefGoogle Scholar
  17. 17.
    Sung Y H, Kwak B M. Reliability bound based on the maximum entropy principle with respect to the first truncated moment. Journal of Mechanical Science and Technology, 2010, 24(9): 1891–1900CrossRefGoogle Scholar
  18. 18.
    Shi X, Teixeira A P, Zhang J, et al. Structural reliability analysis based on probabilistic response modelling using the maximum entropy method. Engineering Structures, 2014, 70: 106–116CrossRefGoogle Scholar
  19. 19.
    Chatzis S P, Andreou A S. Maximum entropy discrimination Poisson regression for software reliability modeling. IEEE Transactions on Neural Networks and Learning Systems, 2015, 26(11): 2689–2701MathSciNetCrossRefGoogle Scholar
  20. 20.
    Zhang Y, Liu Q. Reliability-based design of automobile components. Proceedings of the Institution of Mechanical Engineers. Part D, Journal of Automobile Engineering, 2002, 216(6): 455–471CrossRefGoogle Scholar
  21. 21.
    Zhang Y, He X, Liu Q, et al. Reliability sensitivity of automobile components with arbitrary distribution parameters. Proceedings of the Institution of Mechanical Engineers. Part D, Journal of Automobile Engineering, 2005, 219(2): 165–182CrossRefGoogle Scholar
  22. 22.
    Zhang Y. Reliability-based robust design optimization of vehicle components, Part I: Theory. Frontiers of Mechanical Engineering, 2015, 10(2): 138–144CrossRefGoogle Scholar
  23. 23.
    Zhang Y. Reliability-based robust design optimization of vehicle components, Part II: Case studies. Frontiers of Mechanical Engineering, 2015, 10(2): 145–153CrossRefGoogle Scholar

Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Equipment Reliability InstituteShenyang University of Chemical TechnologyShenyangChina

Personalised recommendations