Reliability analysis and optimization design on equilibrium elbow

  • Jie ZhouEmail author
  • Yun-Xian Jia
  • Jie Li
Original Article


Equilibrium elbow is a key mechanical component in the self-propelled artillery system and the reliability analysis of the component is necessary to the safety of the whole system. In this paper, the equilibrium elbow model is established to analyze the reliability and reliability sensitivity of arbitrary distribution parameters. Three main failure modes and the times of loading action have been taken into account when analyzing the reliability sensitivity. Numerical method for reliability calculation is presented based on four moment method and the reliability sensitivity model of mean and variance values with random structural parameters were established. Based on the results of the reliability sensitivity analysis, reliability robust optimization design has been studied to enhance the reliability of equilibrium elbow and decrease the reliability sensitivity of mean and variance value. Application of the proposed approach could provide a practical routine for mechanical optimization and design.


Equilibrium elbow Reliability sensitivity Optimization design 



The research work is supported by National Natural Science Foundation of China (71401173).


  1. Boutsikas V, Koutras V (2002) On a class of multiple failure modes systems. Nav Res Logist 49(2):167–185MathSciNetCrossRefGoogle Scholar
  2. Cao Y, Xu C, Xu Y (2016) Collaborative optimization method of trajectory and gun for wheeled self-propelled gun. Trans Beijing Inst Technol 36(5):446–451MathSciNetGoogle Scholar
  3. Hu J, Ge X, Zhang L et al (2014) Degradation shift modeling and condition maintenance decision optimization of multi-failure system. Comput Integr Manuf Syst 20(1):165–172 (in Chinese) Google Scholar
  4. Jiang L, Feng QM, Coit DW (2012) Reliability and maintenance modeling for dependent competing failure processes with shifting failure thresholds. IEEE Trans Reliab 61(4):932–945CrossRefGoogle Scholar
  5. Levitin G (2001) Incorporating common cause failures into nor-repairable multi-state series-parallel system analysis. IEEE Trans Reliab 50(4):380–388MathSciNetCrossRefGoogle Scholar
  6. Li JP, Thompson GA (2005) Method to take account of in-homogeneity in mechanical component reliability calculations. IEEE Trans Reliab 54(1):159–168CrossRefGoogle Scholar
  7. Li H, Lü F, Lin F et al (2012) High energy storage density capacitors in pulsed power application. High Power Laser Particle Beams 24(3):554–558 (in Chinese) CrossRefGoogle Scholar
  8. Liu C, Tan F, Wang L (2015) Research on multi-objective optimization of machine bed based on sensitivity analysis. Modul Mach Tool Autom Manuf Tech 3:1–4Google Scholar
  9. Liu Y, Li T, Liu K, Zhang Y (2016) Chatter reliability prediction of turning process system with uncertainties.  Mech Syst Signal Process 66(1):232–247CrossRefGoogle Scholar
  10. Pickard K, Muller P, Bertsche B (2005) Multiple failure mode and effects analysis: an approach to risk assessment of multiple failures with FMEA. In: Proceedings of reliability and maintainability symposium. Washington, USA. IEEE, 2005, pp 457–462Google Scholar
  11. Ramirez-Marquez JE, David WC (2007) Optimization of system reliability in the presence of common cause failures. Reliability Engineering & System Safety 92(10):1421–1434CrossRefGoogle Scholar
  12. Shi W, Li W (2016) Fracture failure analysis of ZTC10 titanium alloy balance elbow. Fail Anal Prev 11(5):300–321Google Scholar
  13. Si YY, Sun ZL, Yan M (2009) Application of response surface methodology in sensitivity calculation of reliability. J Northeast Univ (Nat Sci) 30(2):270–273Google Scholar
  14. Song SL, Coit DW, Feng QM et al (2014) Reliability analysis for multi-component systems subject to multiple dependent competing failure processes. IEEE Trans Reliab 63(1):331–345CrossRefGoogle Scholar
  15. Sun W, Ma B, Ma J, Zhao Y (2014) Reliability analysis of suspension device in the refit of a tracked vehicle. Noise Vib Control 34(4):165–168Google Scholar
  16. Wang WB, Banjevic D, Pecht M (2010) A multi-component and multi-failure mode inspection model based on the delay time concept. Reliab Eng Syst Saf 95(8):912–920CrossRefGoogle Scholar
  17. Wang QL, Wang HY, Rui Q (2012) Dynamic modeling and simulation analysis on ride dynamic of wheeled off-road vehicle. J Acad Armored Force Eng 26(5):34–38 (in Chinese)Google Scholar
  18. Xie L, Zhou J, Hao C (2004) System level load-strength interference based reliability modeling of k-out-of-n system. Reliab Eng Syst Saf 84(3):311–317CrossRefGoogle Scholar
  19. Xing L, Meshkat L, Donohue SK (2007) Reliability analysis of hierarchical computer-based system subject to common-cause failures. Reliab Eng Syst Saf 92(3):351–359CrossRefGoogle Scholar
  20. Yang QY, Hong YL, Chen Y et al (2012) Failure profile analysis of complex repairable systems with multiple failure modes. IEEE Trans Reliab 61(1):180–191CrossRefGoogle Scholar
  21. Yang J, Zhao Y, Cai H et al (2015) Reasonable load sets for design assessment on journal/axle box bearings of railway vehicles related to probabilistic lives. J Mech Eng 51(18):191–197CrossRefGoogle Scholar
  22. Zhang M, Feng F (2005) The Conjunction connect Load-arm with Damper of One High-Speed Track Vehicle Improvement. Vehicle & Power Technology 97(1):36–38Google Scholar
  23. Zhang Y, Lyu H (2014) An analytical methodology of reliability and sensitivity analysis for mechanical components considering the times of load action. J Eng Des 21(2):119–123Google Scholar
  24. Zhang Y, Tang J, Zhang M, Lin C (2008) Research on reliability simulation process model based on Monte Carlo method. Syst Eng Electron 30(7):1374–1385 (in Chinese)Google Scholar
  25. Zhang Y, Cao H, Wang H, Yang Z (2015) Reliability and reliability sensitivity analyses of cutting precision based on a lathe spindle’s dynamic responses. J Vib Shock 34(23):14–17 (in Chinese)Google Scholar

Copyright information

© The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringArmy Engineering UniversityShijiazhuangPeople’s Republic of China
  2. 2.Anhui UniversityHefeiPeople’s Republic of China

Personalised recommendations