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Applications of Samaniego Signatures to Bounds on Variances of Coherent and Mixed System Lifetimes

In: Recent Advances in System Reliability

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  • Tomasz Rychlik

    (Polish Academy of Sciences)

Abstract

Using the notion of Samaniego signature, we present bounds on lifetime variances for coherent and mixed systems composed of items with exchangeable and i.i.d. lifetimes. In the exchangeable case, we present characterizations of lifetime distributions of k-out-of-n and some more general systems, dependent on the component lifetime distribution, and apply them for calculating bounds on system lifetime variances, dependent on either the component lifetime distribution or its variance. In the i.i.d. case, for arbitrary mixed system we provide upper bounds on its lifetime variance, expressed in the single component variance units. Moreover, for fixed lifetime distributions, we describe mixed systems with minimal and maximal lifetime variances.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:ssrchp:978-1-4471-2207-4_5
    DOI: 10.1007/978-1-4471-2207-4_5
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    Cited by:

    1. 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.

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