Copula-Based Approach to Reliability Analysis of Phased-Mission Systems

Document Type : Original Research Article

Authors

Department of Operational Research, University of Delhi, Delhi-7, India

Abstract

A phased-mission system (PMS) involves several different tasks or phases that must be accomplished in sequence. The system configuration, task success criteria, and component failure characteristics may vary from phase to phase. Consequently, the reliability evaluation of PMSs is more challenging than that of single-phase in the field of system reliability analysis. The paper deals with the reliability evaluation of non-repairable Phased-Mission Systems with three phases and five phases involving dependent components in each phase.  The cumulative exposure model has been used to model a PMS, and the dependency between components of a system in a phase is modeled using the Gumbel-Hougaard copula. Reliability importance analyses of the 3-PMS and  5-PMS  have also been carried out. The method developed has been illustrated using numerical examples. The proposed methodology can also be generalized to PMSs with more than five phases.

Keywords

Main Subjects

References

  1. K. Somani, J. A. Ritcey, and S. H. Au, "Computationally-efficient phased-mission reliability analysis for systems with variable configurations," IEEE Transactions on Reliability, vol. 41, no. 4, pp. 504-511, 1992.
  2. Xing, "Reliability evaluation of phased-mission systems with imperfect fault coverage and common-cause failures," IEEE Transactions on Reliability, vol. 56, no. 1, pp. 58-68, 2007.
  3. Alam, M. Song, S. Hester, and T. Seliga, "Reliability analysis of phased-mission systems: a practical approach," in RAMS'06. Annual Reliability and Maintainability Symposium, 2006., 2006, pp. 551-558: IEEE.
  4. D. Esary and H. Ziehms, "Reliability analysis of phased missions," NAVAL POSTGRADUATE SCHOOL MONTEREY CA1975.
  5. Bondavalli, I. Mura, and M. Nelli, "Analytical modelling and evaluation of phased-mission systems for space applications," in Proceedings 1997 High-Assurance Engineering Workshop, 1997, pp. 85-91: IEEE.
  6. Xing and S. V. Amari, "Reliability of phased-mission systems," Handbook of performability engineering, pp. 349-368, 2008.
  7. Xing and G. Levitin, "BDD-based reliability evaluation of phased-mission systems with internal/external common-cause failures," Reliability Engineering & System Safety, vol. 112, pp. 145-153, 2013.
  8. Peng, Q. Zhai, L. Xing, and J. Yang, "Reliability of demand-based phased-mission systems subject to fault level coverage," Reliability Engineering & System Safety, vol. 121, pp. 18-25, 2014.
  9. Huang, L. J. Aslett, and F. P. Coolen, "Reliability analysis of general phased mission systems with a new survival signature," Reliability Engineering & System Safety, vol. 189, pp. 416-422, 2019.
  10. Kim and K. S. Park, "Phased-mission system reliability under Markov environment," IEEE Transactions on reliability, vol. 43, no. 2, pp. 301-309, 1994.
  11. Xing and S. V. Amari, Binary decision diagrams and extensions for system reliability analysis. John Wiley & Sons, 2015.
  12. V. Amari, C. Wang, L. Xing, and R. Mohammad, "An efficient phased-mission reliability model considering dynamic k-out-of-n subsystem redundancy," IISE Transactions, vol. 50, no. 10, pp. 868-877, 2018.
  13. -Y. Li, Y.-F. Li, H.-Z. Huang, and E. Zio, "Reliability assessment of phased-mission systems under random shocks," Reliability Engineering & System Safety, vol. 180, pp. 352-361, 2018.
  14. Zhai, L. Xing, R. Peng, and J. Yang, "Aggregated combinatorial reliability model for non-repairable parallel phased-mission systems," Reliability Engineering & System Safety, vol. 176, pp. 242-250, 2018.
  15. Wang, L. Xing, S. V. Amari, and B. Tang, "Efficient reliability analysis of dynamic k-out-of-n heterogeneous phased-mission systems," Reliability Engineering & System Safety, vol. 193, p. 106586, 2020.
  16. -Y. Li, X. Xiong, J. Guo, H.-Z. Huang, and X. Li, "Reliability assessment of non-repairable multi-state phased mission systems with backup missions," Reliability Engineering & System Safety, vol. 223, p. 108462, 2022.
  17. B. Nelsen, An introduction to copulas. Springer science & business media, 2007.
  18. Zhou, Z. Lu, Y. Shi, and K. Cheng, "The copula-based method for statistical analysis of step-stress accelerated life test with dependent competing failure modes," Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk Reliability, vol. 233, no. 3, pp. 401-418, 2019.
  19. Jia, L. Xing, and G. Li, "Copula‐based reliability and safety analysis of safety‐critical systems with dependent failures," Quality and Reliability Engineering International, vol. 34, no. 5, pp. 928-938, 2018.
  20. Zhang, Y. Sun, and L. Zhong, "Copula function-based reliability analysis of a series system with a single cold standby unit," Acta Aeronautica Et Astronautica Sinica, vol. 35, no. 8, pp. 2207-16, 2014.
  21. Nelson, Accelerated Testing: Statistical Models, Test Plans, and Data Analysis. Wiley, 1990.
  22. Zang, N. Sun, and K. S. Trivedi, "A BDD-based algorithm for reliability analysis of phased-mission systems," IEEE Transactions on Reliability, vol. 48, no. 1, pp. 50-60, 1999.
  23. Mural, A. Bondavalli, X. Zang, and K. Trivedi, "Dependability modeling and evaluation of phased mission systems: a DSPN approach," in Dependable computing for critical applications 7, 1999, pp. 319-337: IEEE.
  24. B. Nelsen, "Some properties of Schur-constant survival models and their copulas," Brazilian Journal of Probability Statistics, pp. 179-190, 2005.
  25. P. Zhang, J. Z. Shang, X. Chen, C. H. Zhang, and Y. S. Wang, "Statistical inference of accelerated life testing with dependent competing failures based on copula theory," IEEE Transactions on Reliability, vol. 63, no. 3, pp. 764-780, 2014.
  26. K. Vaurio, "Importance measures for multi-phase missions," Reliability Engineering & System Safety, vol. 96, no. 1, pp. 230-235, 2011.
  27. Huang, F. P. Coolen, T. Coolen-Maturi, and Y. Zhang, "A new study on reliability importance analysis of phased mission systems," IEEE Transactions on Reliability, vol. 69, no. 2, pp. 522-532, 2019.
International Journal of Reliability, Risk and Safety: Theory and Application
Volume 5, Issue 2
December 2022
Pages 49-62

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History

  • Receive Date: 30 November 2022
  • Revise Date: 24 January 2023
  • Accept Date: 03 February 2023

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