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

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Abstract

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.

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References

  1. Kapur K C, Lamberson L R. Reliability in Engineering Design. New York: John Wiley & Sons, 1977

    Google Scholar 

  2. Dhillon B S, Singh C. Engineering Reliability. New York: John Wiley & Sons, 1981

    MATH  Google Scholar 

  3. Henley E J, Kumamoto H. Reliability Engineering and Risk Assessment. Englewood Cliffs: Prentice-Hall Inc., 1981

    Google Scholar 

  4. O’Connor P D T. Practical Reliability Engineering. New York: John Wiley & Sons, 1984

    Google Scholar 

  5. Wasserman G S. Reliability Verification, Testing, and Analysis in Engineering Design. New York: Marcel Dekker, Inc., 2002

    Book  Google Scholar 

  6. Ang A H S, Tang W H. Probability Concepts in Engineering Planning and Design. New York: John Wiley & Sons, 2006

    Google Scholar 

  7. Elsayed A E. Reliability Engineering. 2nd ed. New York: John Wiley & Sons, 2012

    MATH  Google Scholar 

  8. Klyatis L M. Accelerated Reliability and Durability Testing Technology. New York: John Wiley & Sons, 2012

    MATH  Google Scholar 

  9. Zhang Y. Reliability Design of Automobile Components. Beijing: Beijing Institute of Technology Press, 2000 (in Chinese)

    Google Scholar 

  10. Zhang Y. Introduction of Mechanical Reliability. Beijing: Science Press, 2012 (in Chinese)

    Google Scholar 

  11. Zhang Y. Reliability-based design for automobiles in China. Frontiers of Mechanical Engineering in China, 2008, 3(4): 369–376

    Article  Google Scholar 

  12. Zhang Y. Connotation and development of mechanical reliabilitybased design. Chinese Journal of Mechanical Engineering, 2010, 46 (14): 167–188

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  14. Zhang Y, Sun Z. The reliability syllabus of mechanical products. Journal of Mechanical Engineering, 2014, 50(14): 14–20 (in Chinese)

    Article  Google Scholar 

  15. Siddall J N. Optimal Engineering Design: Principles and Application. New York: Marcel Dekker, 1982

    Google Scholar 

  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): 781–795

    Article  Google Scholar 

  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): 1891–1900

    Article  Google Scholar 

  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: 106–116

    Article  Google Scholar 

  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): 2689–2701

    Article  MathSciNet  Google Scholar 

  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): 455–471

    Article  Google Scholar 

  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): 165–182

    Article  Google Scholar 

  22. Zhang Y. Reliability-based robust design optimization of vehicle components, Part I: Theory. Frontiers of Mechanical Engineering, 2015, 10(2): 138–144

    Article  Google Scholar 

  23. Zhang Y. Reliability-based robust design optimization of vehicle components, Part II: Case studies. Frontiers of Mechanical Engineering, 2015, 10(2): 145–153

    Article  Google Scholar 

Download references

Acknowledgements

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

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  1. Equipment Reliability Institute, Shenyang University of Chemical Technology, Shenyang, 110142, China

    Yimin Zhang

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  1. Yimin Zhang
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Correspondence to Yimin Zhang.

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Zhang, Y. Principle of maximum entropy for reliability analysis in the design of machine components. Front. Mech. Eng. 14, 21–32 (2019). https://doi.org/10.1007/s11465-018-0512-z

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  • DOI: https://doi.org/10.1007/s11465-018-0512-z

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