IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v92y2007i3p300-307.html
   My bibliography  Save this article

Analytical method for reliability and MTTF assessment of coherent systems with dependent components

Author

Listed:
  • Cui, Lirong
  • Li, Haijun

Abstract

This paper discusses engineering systems with structural as well as failure dependence among their components. Using the Markov process approach, a coherent system of components with multivariate phase type life distribution is introduced to model the components working in a common random environment. The phase type model is flexible enough to comprise many realistic situations, and also manages to yield the explicit matrix representations of the system reliability measures. Some examples are also presented to illustrate the fact that ignoring the failure dependence among the components often results in over-estimating or under-estimating the system reliability.

Suggested Citation

  • Cui, Lirong & Li, Haijun, 2007. "Analytical method for reliability and MTTF assessment of coherent systems with dependent components," Reliability Engineering and System Safety, Elsevier, vol. 92(3), pages 300-307.
    • Handle: RePEc:eee:reensy:v:92:y:2007:i:3:p:300-307
    DOI: 10.1016/j.ress.2006.04.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832006000950
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2006.04.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Vaurio, Jussi K., 2005. "Uncertainties and quantification of common cause failure rates and probabilities for system analyses," Reliability Engineering and System Safety, Elsevier, vol. 90(2), pages 186-195.
    2. Li, Haijun, 2003. "Association of multivariate phase-type distributions, with applications to shock models," Statistics & Probability Letters, Elsevier, vol. 64(4), pages 381-392, October.
    3. V. S. S. Yadavalli & A. Bekker & J. Pauw, 2005. "Bayesian Study Of A Two-Component System With Common-Cause Shock Failures," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 22(01), pages 105-119.
    4. David Assaf & Naftali A. Langberg & Thomas H. Savits & Moshe Shaked, 1984. "Multivariate Phase-Type Distributions," Operations Research, INFORMS, vol. 32(3), pages 688-702, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Villén-Altamirano, José, 2010. "RESTART simulation of non-Markov consecutive-k-out-of-n: F repairable systems," Reliability Engineering and System Safety, Elsevier, vol. 95(3), pages 247-254.
    2. Konul Bayramoglu Kavlak, 2017. "Reliability and mean residual life functions of coherent systems in an active redundancy," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(1), pages 19-28, February.
    3. Duan, Chaoqun & Makis, Viliam & Deng, Chao, 2020. "A two-level Bayesian early fault detection for mechanical equipment subject to dependent failure modes," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    4. Zhang, Chao & Xu, Xin & Dui, Hongyan, 2020. "Analysis of network cascading failure based on the cluster aggregation in cyber-physical systems," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    5. Moustafa Magdi S., 2008. "MTBF for K-out-of-N: G Systems with M Failure Modes," Stochastics and Quality Control, De Gruyter, vol. 23(2), pages 219-226, January.
    6. Eryılmaz, Serkan, 2009. "Reliability properties of consecutive k-out-of-n systems of arbitrarily dependent components," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 350-356.
    7. Dong Lyu & Shubin Si & Zhiqiang Cai & Liyang Xie, 2020. "Computational method for importance measure of the k-out-of-n system based on stress–strength interference," Journal of Risk and Reliability, , vol. 234(1), pages 27-40, February.
    8. Liu, Yu & Liu, Qinzhen & Xie, Chaoyang & Wei, Fayuan, 2019. "Reliability assessment for multi-state systems with state transition dependency," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 276-288.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Qi-Ming He & Jiandong Ren, 2016. "Analysis of a Multivariate Claim Process," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 257-273, March.
    2. Cai, Jun & Li, Haijun, 2005. "Multivariate risk model of phase type," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 137-152, April.
    3. Li, Haijun, 2003. "Association of multivariate phase-type distributions, with applications to shock models," Statistics & Probability Letters, Elsevier, vol. 64(4), pages 381-392, October.
    4. Eisele, Karl-Theodor, 2008. "Recursions for multivariate compound phase variables," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 65-72, February.
    5. Asimit, Alexandru V. & Jones, Bruce L., 2007. "Extreme behavior of multivariate phase-type distributions," Insurance: Mathematics and Economics, Elsevier, vol. 41(2), pages 223-233, September.
    6. Min Zhang & Zhijian Zhang & Ali Mosleh & Sijuan Chen, 2017. "Common cause failure model updating for risk monitoring in nuclear power plants based on alpha factor model," Journal of Risk and Reliability, , vol. 231(3), pages 209-220, June.
    7. Gianpaolo Di Bona & Antonio Forcina & Domenico Falcone & Luca Silvestri, 2020. "Critical Risks Method (CRM): A New Safety Allocation Approach for a Critical Infrastructure," Sustainability, MDPI, vol. 12(12), pages 1-19, June.
    8. Abou, Seraphin C., 2010. "Performance assessment of multi-state systems with critical failure modes: Application to the flotation metallic arsenic circuit," Reliability Engineering and System Safety, Elsevier, vol. 95(6), pages 614-622.
    9. Surya, Budhi Arta, 2022. "Conditional multivariate distributions of phase-type for a finite mixture of Markov jump processes given observations of sample path," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    10. Bo Friis Nielsen, 2022. "Characterisation of multivariate phase type distributions," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 229-231, April.
    11. Hoepfer, V.M. & Saleh, J.H. & Marais, K.B., 2009. "On the value of redundancy subject to common-cause failures: Toward the resolution of an on-going debate," Reliability Engineering and System Safety, Elsevier, vol. 94(12), pages 1904-1916.
    12. Cheung, Eric C.K. & Peralta, Oscar & Woo, Jae-Kyung, 2022. "Multivariate matrix-exponential affine mixtures and their applications in risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 364-389.
    13. Woo, Jae-Kyung, 2016. "On multivariate discounted compound renewal sums with time-dependent claims in the presence of reporting/payment delays," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 354-363.
    14. Roel Verbelen & Katrien Antonio & Gerda Claeskens, 2016. "Multivariate mixtures of Erlangs for density estimation under censoring," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(3), pages 429-455, July.
    15. Eric C. K. Cheung & Oscar Peralta & Jae-Kyung Woo, 2021. "Multivariate matrix-exponential affine mixtures and their applications in risk theory," Papers 2201.11122, arXiv.org.
    16. Hsu, Ying-Lin & Lee, Ssu-Lang & Ke, Jau-Chuan, 2009. "A repairable system with imperfect coverage and reboot: Bayesian and asymptotic estimation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2227-2239.
    17. KanÄ ev, DuÅ¡ko & ÄŒepin, Marko, 2012. "A new method for explicit modelling of single failure event within different common cause failure groups," Reliability Engineering and System Safety, Elsevier, vol. 103(C), pages 84-93.
    18. Veljanovski, N. & ÄŒepin, M., 2024. "Event tree-based risk and financial assessment for power plants," Reliability Engineering and System Safety, Elsevier, vol. 247(C).
    19. Haijun Li & Susan Xu & Way Kuo, 2014. "Asymptotic analysis of simultaneous damages in spatial Boolean models," Annals of Operations Research, Springer, vol. 212(1), pages 139-154, January.
    20. L Xing & P Boddu & Y Sun & W Wang, 2010. "Reliability analysis of static and dynamic fault-tolerant systems subject to probabilistic common-cause failures," Journal of Risk and Reliability, , vol. 224(1), pages 43-53, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:reensy:v:92:y:2007:i:3:p:300-307. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.