IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v32y2017i4d10.1007_s00180-017-0718-2.html
   My bibliography  Save this article

The joint signature of parallel systems for different permutations of failure times

Author

Listed:
  • Leila Mohammadi

    (Leiden University)

Abstract

The joint signature of m coherent systems is an extension of the joint signature of two systems introduced in 2010. It is interesting because the joint signature depends only on the mechanism of the systems’ composition rather than the underlying distribution function of the component lifetimes. It also depends on the permutation of the failure times. As there are m! permutations we need to compute m! joint signatures, many of which are the same. Even if the joint signatures for two different orderings of the system lifetimes are different, it is sometimes possible to obtain one of them via the other one by a transformation. In this article, we consider several parallel systems with independent and identically distributed component lifetimes and investigate how to classify the m! permutations of the failure times according to the same joint signature. Further, we partition the result into sets based on transformed joint signatures. Moreover, we establish a relationship between the different sets in the last partition so that the related joint signatures can be converted into each other by small modifications. By this procedure, we are able to compute the m! joint signatures together efficiently. Using several examples, we illustrate that our classifications save us a large number of calculations. We introduce an algorithm to determine the partitions and present a computer program for the algorithm. The case of series-parallel systems is quite complicated and is discussed briefly.

Suggested Citation

  • Leila Mohammadi, 2017. "The joint signature of parallel systems for different permutations of failure times," Computational Statistics, Springer, vol. 32(4), pages 1727-1746, December.
    • Handle: RePEc:spr:compst:v:32:y:2017:i:4:d:10.1007_s00180-017-0718-2
    DOI: 10.1007/s00180-017-0718-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-017-0718-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-017-0718-2?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. Francisco J. Samaniego, 2007. "System Signatures and their Applications in Engineering Reliability," International Series in Operations Research and Management Science, Springer, number 978-0-387-71797-5, December.
    2. Da, Gaofeng & Zheng, Ben & Hu, Taizhong, 2012. "On computing signatures of coherent systems," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 142-150, January.
    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. Leila Mohammadi, 2017. "The joint signature of coherent systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(7), pages 566-579, October.

    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. Gaofeng Da & Lvyu Xia & Taizhong Hu, 2014. "On Computing Signatures of k-out-of-n Systems Consisting of Modules," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 223-233, March.
    2. Zarezadeh, S. & Mohammadi, L. & Balakrishnan, N., 2018. "On the joint signature of several coherent systems with some shared components," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1092-1100.
    3. Marichal, Jean-Luc & Mathonet, Pierre & Spizzichino, Fabio, 2015. "On modular decompositions of system signatures," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 19-32.
    4. Jia, Xujie & Shen, Jingyuan & Xu, Fanqi & Ma, Ruihong & Song, Xueying, 2019. "Modular decomposition signature for systems with sequential failure effect," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 435-444.
    5. Sadiya & Mangey Ram & Akshay Kumar, 2022. "A New Approach to Compute System Reliability with Three-Serially Linked Modules," Mathematics, MDPI, vol. 11(1), pages 1-18, December.
    6. Qin, Jinlei & Coolen, Frank P.A., 2022. "Survival signature for reliability evaluation of a multi-state system with multi-state components," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    7. Frank PA Coolen & Tahani Coolen-Maturi & Abdullah H Al-nefaiee, 2014. "Nonparametric predictive inference for system reliability using the survival signature," Journal of Risk and Reliability, , vol. 228(5), pages 437-448, October.
    8. Marichal, Jean-Luc & Mathonet, Pierre, 2013. "Computing system signatures through reliability functions," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 710-717.
    9. Abdullah H Al-nefaiee & Frank PA Coolen, 2013. "Nonparametric predictive inference for system failure time based on bounds for the signature," Journal of Risk and Reliability, , vol. 227(5), pages 513-522, October.
    10. He Yi & Lirong Cui, 2018. "A new computation method for signature: Markov process method," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(5), pages 410-426, August.
    11. Leila Mohammadi, 2017. "The joint signature of coherent systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(7), pages 566-579, October.
    12. Erhard Cramer & Jorge Navarro, 2015. "Progressive Type‐II censoring and coherent systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(6), pages 512-530, September.
    13. Feng, Geng & Patelli, Edoardo & Beer, Michael & Coolen, Frank P.A., 2016. "Imprecise system reliability and component importance based on survival signature," Reliability Engineering and System Safety, Elsevier, vol. 150(C), pages 116-125.
    14. Hindolo George-Williams & Geng Feng & Frank PA Coolen & Michael Beer & Edoardo Patelli, 2019. "Extending the survival signature paradigm to complex systems with non-repairable dependent failures," Journal of Risk and Reliability, , vol. 233(4), pages 505-519, August.
    15. Zhengcheng Zhang & N. Balakrishnan, 2016. "Representations of the inactivity time for coherent systems with heterogeneous components and some ordered properties," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(1), pages 113-126, January.
    16. Bo H. Lindqvist & Francisco J. Samaniego, 2019. "Some new results on the preservation of the NBUE and NWUE aging classes under the formation of coherent systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(5), pages 430-438, August.
    17. Tomasz J. Kozubowski & Krzysztof Podgórski, 2018. "Kumaraswamy Distribution and Random Extrema," The Open Statistics and Probability Journal, Bentham Open, vol. 9(1), pages 18-25, July.
    18. Coolen, Frank P.A. & Coolen-Maturi, Tahani, 2015. "Predictive inference for system reliability after common-cause component failures," Reliability Engineering and System Safety, Elsevier, vol. 135(C), pages 27-33.
    19. Marichal, Jean-Luc & Mathonet, Pierre, 2013. "On the extensions of Barlow–Proschan importance index and system signature to dependent lifetimes," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 48-56.
    20. M. Burkschat & J. Navarro, 2014. "Asymptotic behavior of the hazard rate in systems based on sequential order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(8), pages 965-994, November.

    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:spr:compst:v:32:y:2017:i:4:d:10.1007_s00180-017-0718-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.