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On the joint signature of several coherent systems with some shared components

Author

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  • Zarezadeh, S.
  • Mohammadi, L.
  • Balakrishnan, N.

Abstract

The concept of joint signature (JS), introduced by Navarro, Samaniego, and Balakrishnan (2010), is a useful tool for investigating the joint reliability of two coherent systems with shared components. In this article, by considering several coherent systems which share some components, with independent and identically distributed lifetimes, we obtain a pseudo-mixture representation for the joint distribution of the systems lifetimes based on a general notion of joint signature which is referred to as generalized joint signature (GJS). It is shown how the GJS is separated from the effect of the components’ lifetime distribution and this relationship helps us to represent the GJS as a two-dimensional matrix instead of a high-dimensional one. Based on the GJS, some ordering results are obtained for comparing two clusters of coherent systems with some shared components. Several examples are provided to illustrate the results established here.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:264:y:2018:i:3:p:1092-1100
    DOI: 10.1016/j.ejor.2017.06.066
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    References listed on IDEAS

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    7. Zarezadeh, S. & Asadi, M. & Balakrishnan, N., 2014. "Dynamic network reliability modeling under nonhomogeneous Poisson processes," European Journal of Operational Research, Elsevier, vol. 232(3), pages 561-571.
    8. Navarro, Jorge & Rychlik, Tomasz, 2007. "Reliability and expectation bounds for coherent systems with exchangeable components," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 102-113, January.
    9. 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.
    10. Navarro, Jorge & Pellerey, Franco & Di Crescenzo, Antonio, 2015. "Orderings of coherent systems with randomized dependent components," European Journal of Operational Research, Elsevier, vol. 240(1), pages 127-139.
    11. Borgonovo, Emanuele & Aliee, Hananeh & Glaß, Michael & Teich, Jürgen, 2016. "A new time-independent reliability importance measure," European Journal of Operational Research, Elsevier, vol. 254(2), pages 427-442.
    12. Gupta, Nitin & Misra, Neeraj & Kumar, Somesh, 2015. "Stochastic comparisons of residual lifetimes and inactivity times of coherent systems with dependent identically distributed components," European Journal of Operational Research, Elsevier, vol. 240(2), pages 425-430.
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    Cited by:

    1. Zarezadeh, Somayeh & Asadi, Majid, 2019. "Coherent systems subject to multiple shocks with applications to preventative maintenance," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 124-132.
    2. Jørgen Vitting Andersen & Roy Cerqueti & Jessica Riccioni, 2023. "Rational expectations as a tool for predicting failure of weighted k-out-of-n reliability systems," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03634370, HAL.
    3. Eryilmaz, Serkan, 2020. "Age-based preventive maintenance for coherent systems with applications to consecutive-k-out-of-n and related systems," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    4. Coolen-Maturi, Tahani & Coolen, Frank P.A. & Balakrishnan, Narayanaswamy, 2021. "The joint survival signature of coherent systems with shared components," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    5. Jørgen Vitting Andersen & Roy Cerqueti & Jessica Riccioni, 2023. "Rational expectations as a tool for predicting failure of weighted k-out-of-n reliability systems," Post-Print hal-03634370, HAL.
    6. Jørgen Vitting Andersen & Roy Cerqueti & Giulia Rotundo, 2017. "Rational expectations and stochastic systems," Documents de travail du Centre d'Economie de la Sorbonne 17060, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Oct 2019.
    7. Zhu, Xiaojun & Balakrishnan, N., 2023. "Non-parametric inference based on reliability life-test of non-identical coherent systems with application to warranty time," Reliability Engineering and System Safety, Elsevier, vol. 232(C).
    8. Yin, Juan & Cui, Lirong & Sun, Yudao & Balakrishnan, Narayanaswamy, 2022. "Reliability modelling for linear and circular k-out-of-n: F systems with shared components," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    9. Juan Yin & Narayanaswamy Balakrishnan & Lirong Cui, 2024. "Efficient reliability computation of consecutive- k -out-of- n : F systems with shared components," Journal of Risk and Reliability, , vol. 238(1), pages 122-135, February.
    10. He Yi & Narayanaswamy Balakrishnan & Lirong Cui, 2022. "On Dependent Multi-State Semi-Coherent Systems Based on Multi-State Joint Signature," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1717-1734, September.
    11. Somayeh Ashrafi & Majid Asadi & Jorge Navarro, 2022. "Joint Reliability Function of Coherent Systems with Shared Heterogeneous Components," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1485-1502, September.
    12. Yi, He & Balakrishnan, Narayanaswamy & Li, Xiang, 2024. "Joint reliability of linear consecutive k-type systems with shared components in a zigzag structure," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    13. Jorgen-Vitting Andersen & Roy Cerqueti & Jessica Riccioni, 2023. "Rational expectations as a tool for predicting failure of weighted k-out-of-n reliability systems," Annals of Operations Research, Springer, vol. 326(1), pages 295-316, July.

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