Preservation of some partial orderings under the formation of coherent systems

Nanda, Asok K.; Jain, Kanchan; Singh, Harshinder

doi:10.1016/s0167-7152(98)00043-1

Cited by 32 publications

(26 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Suppose the lifetime of the components from C 1 has distribution function F and that from system C 2 has distribution function G. In the following result, the preservation of ≤ lr↑ -order is established for a coherent system with identically distributed components. This is an analogous of Theorem 2.4 of Nanda et al (1998), where the same result is presented in the case of ≤ lrorder.…”

Section: Systems With Iid Componentssupporting

confidence: 66%

See 1 more Smart Citation

Some new results about shifted hazard and shifted likelihood ratio orders

Aboukalam¹,

Kayid²

2007

imf

View full text Add to dashboard Cite

Shifted stochastic orders are a useful tool for establishing interesting inequalities. Two such stochastic orders are the up hazard rate order and the up likelihood ratio order. In this article, we give some results on the preservation of the above orderings between the components under the formation of coherent systems with different structures. Both the cases when components either identically distributed or not necessary identically distributed are discussed. Finally, we provide some applications to Poisson and non-homogeneous Poisson shock models.

show abstract

Section: Systems With Iid Componentssupporting

confidence: 66%

“…As noted in Di Crescenzo and Longobardi (2001), the assumption (3.1) is satisfied by several coherent systems, including the k-out-of-n one (see also Nanda et al (1998) for more details).…”

Section: Proofmentioning

confidence: 83%

Some new results about shifted hazard and shifted likelihood ratio orders

Aboukalam¹,

Kayid²

2007

imf

View full text Add to dashboard Cite

show abstract

“…The condition in (i) earlier was obtained in Theorem 2.2 (c) of for systems with IID components. The function

\overset{α}{falsemml-overline}

is the elasticity of the dual generalized domination function

\overset{H}{falsemml-overline} MathClass-open(u MathClass-close) MathClass-rel= 1 MathClass-bin- H MathClass-open(1 MathClass-bin- u MathClass-close)

.…”

Section: The Main Resultsmentioning

confidence: 85%

Preservation of reliability classes under the formation of coherent systems

Navarro

Aguila

Sordo

et al. 2013

Appl Stoch Models Bus & Ind

View full text Add to dashboard Cite

The preservation of reliability aging classes under the formation of coherent systems is a relevant topic in reliability theory. Thus, it is well known that the new better than used class is preserved under the formation of coherent systems with independent components. However, surprisingly, the increasing failure rate class is not preserved in the independent and identically distributed case, that is, the components may have the (negative) aging increasing failure rate property, but the system does not have this property. In this paper, we study conditions for the preservation of the main reliability classes under the formation of general coherent systems. These results can be applied both for systems with independent or dependent components. We consider both the case of systems with identically distributed components and the case of systems with components having different distributions. Copyright © 2013 John Wiley & Sons, Ltd.

show abstract

“…[3]), whereas conditions (b) and (c) are satisfied for any -out-of-system (see Corollary 3.2 of Misra et al [2], and Corollary 2.1 of Nanda et al [7]). Thus, the above result is valid for -out-of-systems.…”

Section: Becausementioning

confidence: 99%

“…Remark 5: Note that, for any -out-of-system, all the conditions (a), (b), and (c) of Theorem 5 are validated (cf. Barlow and Proschan [5] on p.109, Corollary 2.1 of Nanda et al [7], and Corollary 3.1 of Misra et al [2]). Remark 6: From Counterexample 1, it is seen that the logconcavity condition given in Theorem 5 cannot be removed.…”

Section: Remark 4: From Counterexample 2 It Is Clear That the Log-comentioning

confidence: 99%

Component Redundancy Versus System Redundancy in Different Stochastic Orderings

Hazra

Nanda

2014

IEEE Trans. Rel.

Self Cite

View full text Add to dashboard Cite

Stochastic orders are useful to compare the lifetimes of two systems. We discuss both active redundancy as well as standby redundancy. We show that redundancy at the component level is superior to that at the system level with respect to different stochastic orders, for different types of systems.Index Terms-Coherent system, -out-of-system, reliability, stochastic orders. ACRONYMSAND ABBREVIATIONS st usual stochastic sp stochastic precedence hr hazard rate rhr reversed hazard rate lr likelihood ratio up shifted hazard rate down shifted hazard rate up shifted reversed hazard rate up shifted likelihood ratio down shifted likelihood ratio NOTATION underlying nonnegative random variable probability density function of random variable cumulative distribution function of random variable survival (reliability) function of random variable hazard rate function of random variable reversed hazard rate function of random variable lifetime of a coherent system Manuscript

show abstract

Preservation of some partial orderings under the formation of coherent systems

Cited by 32 publications

References 5 publications

Some new results about shifted hazard and shifted likelihood ratio orders

Some new results about shifted hazard and shifted likelihood ratio orders

Preservation of reliability classes under the formation of coherent systems

Component Redundancy Versus System Redundancy in Different Stochastic Orderings

Contact Info

Product

Resources

About