Stochastic comparisons of residual lifetimes and inactivity times of coherent systems with dependent identically distributed components

Gupta, Nitin; Misra, Neeraj; Kumar, Somesh

doi:10.1016/j.ejor.2014.07.018

Cited by 32 publications

(17 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Stochastic comparisons between these two systems have been made in numerous papers; see e.g. [19], [20], [23], and [33], to name a few. However, to the best of our knowledge, the ageing faster orders have not yet been used as a tool for comparing these two systems.…”

Section: Introductionmentioning

confidence: 99%

On relative ageing of coherent systems with dependent identically distributed components

Hazra

Misra

2020

Adv. Appl. Probab.

Self Cite

View full text Add to dashboard Cite

Relative ageing describes how one system ages with respect to another. The ageing faster orders are used to compare the relative ageing of two systems. Here, we study ageing faster orders in the hazard and reversed hazard rates. We provide some sufficient conditions for one coherent system to dominate another with respect to ageing faster orders. Further, we investigate whether the active redundancy at the component level is more effective than that at the system level with respect to ageing faster orders, for a coherent system. Furthermore, a used coherent system and a coherent system made out of used components are compared with respect to ageing faster orders.

show abstract

Section: Introductionmentioning

confidence: 99%

On relative ageing of coherent systems with dependent identically distributed components

Hazra

Misra

2020

Adv. Appl. Probab.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Being utilized to adjust the probability distribution of random risk so as to put more emphasis to the tail area, the DF h ( u ) and GDF ϕ ( u 1 , ⋯, u n ) are also called distortion functions in theory of risk and actuarial science. For more on them we refer readers to Navarro and Spizzichino (2010), Navarro et al (2013, 2014); Navarro, Pellerey, and Crescenzo (2015), Gupta, Misra, and Kumar (2015), and Navarro (2018).…”

Section: Some Preliminariesmentioning

confidence: 99%

Weak aging properties for coherent systems with statistically dependent component lifetimes

2020

Naval Research Logistics

View full text Add to dashboard Cite

As a relevant topic in reliability theory, the preservation of aging properties under the formation of various coherent structures contributes to improving system performance through better structure design and more effective system maintenance. The classical research in this line usually focuses upon coherent systems with independent component lifetimes. Recently, some authors discussed the preservation of IFR, NBU, and DMRL in the setting of dependent component lifetimes. This paper further investigates sufficient conditions for coherent systems with dependent component lifetimes to preserve aging properties including NBUC, NBU (2), DMRL, and their dual versions. Some examples are presented to illustrate coherent structures and typical copula functions fulfilling the present sufficient conditions as well.

show abstract

“…We consider a 3-out-of-3 system with the lifetimes of components having an Erlang mixture. The shape parameters of the joint distribution are all permutations with repetition of the vector (3,7,12). Then the number of the components of the joint distribution is 27 and all mixing weights are set to be a same value 1 27 .…”

Section: Stochastic Orders Of (N−k+1)-out-of-n Systemmentioning

confidence: 99%

“…For example, [15] adopted Archimedean copula to reflect the dependence among the components. Others may be found in [7], [17], [18] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Conditional Residual Lifetimes of (n-k+1)-out-of n Systems with Mixed Erlang Components

Gui¹

2017

JMS

View full text Add to dashboard Cite

We consider an (n−k+1)-out-of-n system with component lifetimes being correlated. The main objective of this paper is to study the conditional residual lifetime of an (n−k+1)-out-of-n system, given that at a fixed time a certain number of components have failed, assuming that the component lifetimes follow a multivariate Erlang mixture. Comparison studies of the stochastic ordering of the (n−k+1)-out-ofn system are presented. Several examples are presented to illustrate and confirm our results.

show abstract

Stochastic comparisons of residual lifetimes and inactivity times of coherent systems with dependent identically distributed components

Cited by 32 publications

References 23 publications

On relative ageing of coherent systems with dependent identically distributed components

On relative ageing of coherent systems with dependent identically distributed components

Weak aging properties for coherent systems with statistically dependent component lifetimes

Conditional Residual Lifetimes of (n-k+1)-out-of n Systems with Mixed Erlang Components

Contact Info

Product

Resources

About