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Jensen–Shannon information of the coherent system lifetime

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  • Asadi, Majid
  • Ebrahimi, Nader
  • Soofi, Ehsan S.
  • Zohrevand, Younes

Abstract

The signature of a coherent system with n components is an n-dimensional vector whose ith element is the probability that the ith failure of the components is fatal to the system. The signature depends only on the system design and provides useful tools for comparison of systems. We propose the Jensen–Shannon information (JS) criteria for comparison of systems, which is a scalar function of the signature and ranks systems based on their designs. The JS of a system is interpreted in terms of the remaining uncertainty about the system lifetime, the utility of dependence between the lifetime and the number of failures of components fatal to the system, and the Bayesian decision theory. The JS is non-negative and its minimum is attained by k-out-of-n systems, which are the least complex systems. This property offers JS as a measure of complexity of a system. Effects of expansion of a system on JS are studied. Application examples include comparisons of various sets of new systems and used but still working systems discussed in the literature. We also give an upper bound for the JS at the general level and compare it with a known upper bound.

Suggested Citation

  • Asadi, Majid & Ebrahimi, Nader & Soofi, Ehsan S. & Zohrevand, Younes, 2016. "Jensen–Shannon information of the coherent system lifetime," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 244-255.
    • Handle: RePEc:eee:reensy:v:156:y:2016:i:c:p:244-255
    DOI: 10.1016/j.ress.2016.07.015
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    References listed on IDEAS

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    1. Veber, B. & Nagode, M. & Fajdiga, M., 2008. "Generalized renewal process for repairable systems based on finite Weibull mixture," Reliability Engineering and System Safety, Elsevier, vol. 93(10), pages 1461-1472.
    2. Ebrahimi, Nader & Jalali, Nima Y. & Soofi, Ehsan S., 2014. "Comparison, utility, and partition of dependence under absolutely continuous and singular distributions," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 32-50.
    3. Neshat Beheshti & Jeffrey S. Racine & Ehsan S. Soofi, 2015. "Information Measures for Nonparametric Kernel Estimation," Department of Economics Working Papers 2015-03, McMaster University.
    4. 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.
    5. Castet, Jean-Francois & Saleh, Joseph H., 2010. "Single versus mixture Weibull distributions for nonparametric satellite reliability," Reliability Engineering and System Safety, Elsevier, vol. 95(3), pages 295-300.
    6. Eryilmaz, Serkan, 2013. "Mean instantaneous performance of a system with weighted components that have arbitrarily distributed lifetimes," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 290-293.
    7. Shaked, Moshe & Suarez-Llorens, Alfonso, 2003. "On the Comparison of Reliability Experiments Based on the Convolution Order," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 693-702, January.
    8. 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, April.
    9. Eryilmaz, Serkan, 2011. "Estimation in coherent reliability systems through copulas," Reliability Engineering and System Safety, Elsevier, vol. 96(5), pages 564-568.
    10. Chang, Tian Pau, 2011. "Estimation of wind energy potential using different probability density functions," Applied Energy, Elsevier, vol. 88(5), pages 1848-1856, May.
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    Cited by:

    1. 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).
    2. Kharazmi, Omid & Balakrishnan, Narayanaswamy, 2021. "Jensen-information generating function and its connections to some well-known information measures," Statistics & Probability Letters, Elsevier, vol. 170(C).

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