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A note on signature‐based expressions for the entropy of mixed r‐out‐of‐ n systems

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  • Abdolsaeed Toomaj
  • Mahdi Doostparast

Abstract

We provide an expression for the Shannon entropy of mixed r‐out‐of‐ n systems when the lifetimes of the components are independent and identically distributed. The expression gives the system's entropy in terms of the system signature, the distribution and density functions of the lifetime model, and the information measures of the beta distribution. Bounds for the system's entropy are obtained by direct applications of the concavity of the entropy and the information inequality.Copyright © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 202–206, 2014

Suggested Citation

  • Abdolsaeed Toomaj & Mahdi Doostparast, 2014. "A note on signature‐based expressions for the entropy of mixed r‐out‐of‐ n systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(3), pages 202-206, April.
    • Handle: RePEc:wly:navres:v:61:y:2014:i:3:p:202-206
    DOI: 10.1002/nav.21577
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    1. Navarro, Jorge & Rychlik, Tomasz, 2010. "Comparisons and bounds for expected lifetimes of reliability systems," European Journal of Operational Research, Elsevier, vol. 207(1), pages 309-317, November.
    2. Nader Ebrahimi & Ehsan S. Soofi & Refik Soyer, 2010. "Information Measures in Perspective," International Statistical Review, International Statistical Institute, vol. 78(3), pages 383-412, December.
    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. Marek Beśka & Krzysztof Jasiński & Tomasz Rychlik & Marcin Spryszyński, 2012. "Mixed systems with minimal and maximal lifetime variances," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(7), pages 877-894, October.
    5. Tomasz Rychlik, 2012. "Applications of Samaniego Signatures to Bounds on Variances of Coherent and Mixed System Lifetimes," Springer Series in Reliability Engineering, in: Anatoly Lisnianski & Ilia Frenkel (ed.), Recent Advances in System Reliability, chapter 0, pages 63-77, Springer.
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