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

Tomasz Rychlik ()
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Tomasz Rychlik: Polish Academy of Sciences

Chapter Chapter 5 in Recent Advances in System Reliability, 2012, pp 63-77 from Springer

Abstract: 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.

Keywords: Coherent system; Mixed system; k-out-of-n system; Samaniego signature; Order statistic; Exchangeable random variables; i.i.d. random variables (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:ssrchp:978-1-4471-2207-4_5

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DOI: 10.1007/978-1-4471-2207-4_5

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