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On the Kullback Leibler information for mixed systems

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  • A. Toomaj
  • M. Doostparast

Abstract

Entropy and Kullback–Leibler (KL) information for engineering systems have been studied in both statistical and reliability contexts. In this paper, we prove that the KL information between distributions of mixed system lifetimes and the corresponding component lifetimes and also the associated order statistics are distribution free and depends only on the signature of the system provided that lifetimes of components are independent and identically distributed (iid). The obtained results are used to find the closest and the farthest distribution of order statistics from the distribution of the system’s lifetime which is useful to approximate stochastic behaviour of mixed systems when the number of components is large. Finally, we provide bounds and also use the results to obtain a more preferable system among all systems. Some illustrative examples are also given.

Suggested Citation

  • A. Toomaj & M. Doostparast, 2016. "On the Kullback Leibler information for mixed systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(10), pages 2458-2465, July.
    • Handle: RePEc:taf:tsysxx:v:47:y:2016:i:10:p:2458-2465
    DOI: 10.1080/00207721.2014.998744
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    References listed on IDEAS

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    1. Subhash Kochar & Hari Mukerjee & Francisco J. Samaniego, 1999. "The “signature” of a coherent system and its application to comparisons among systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(5), pages 507-523, August.
    2. Jorge Navarro & Francisco J. Samaniego & N. Balakrishnan & Debasis Bhattacharya, 2008. "On the application and extension of system signatures in engineering reliability," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(4), pages 313-327, June.
    3. 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.
    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.
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    Cited by:

    1. Siddhartha Chakraborty & Biswabrata Pradhan, 2024. "On cumulative residual extropy of coherent and mixed systems," Annals of Operations Research, Springer, vol. 340(1), pages 59-81, September.

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