Applications of average and projected systems to the study of coherent systems

Navarro, Jorge; Spizzichino, Fabio; Balakrishnan, N.

doi:10.1016/j.jmva.2010.01.005

Cited by 43 publications

(34 citation statements)

References 21 publications

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“…Other relevant works were shown by Finkelstein [7], Finkelstein and Esaulova [8], Mi [9], Navarro and Hernandez [10], Navarro et al [11], and Navarro et al [12]. Similar results about the mean residual life of mixture can be found in Mi [13] and Navarro and Hernandez [14].…”

Section: Introductionsupporting

confidence: 76%

Limit of hazard rate function of coherent system with discrete life

2010

Appl Stoch Models Bus & Ind

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In this paper we study the limiting behavior of the hazard rate function of a coherent system S whose components are independent and have discrete lifetimes. The lifetime of the system S can be viewed as the lifetime of a parallel system consisting of the series systems obtained from the minimal paths of S. If we appropriately interpret the 'strongest' minimal path(s) of the system S, it will be shown that the limit of the hazard rate functions of S is the same as that of the 'strongest' path(s) of S. The application of the main results are also provided.

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Section: Introductionsupporting

confidence: 76%

Limit of hazard rate function of coherent system with discrete life

2010

Appl Stoch Models Bus & Ind

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“…These representations were used to compare stochastically coherent system lifetimes and to obtain approximations and bounds for their characteristics (see Refs. [20,22,24,25,[27][28][29]36]). Some specific results for consecutive k-out-of-n systems with dependent components were obtained in Ref.…”

Section: Introductionmentioning

confidence: 99%

Coherent systems based on sequential order statistics

Navarro

Burkschat

2011

Naval Research Logistics

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Abstract:The sequential order statistics (SOS) are a good way to model the lifetimes of the components in a system when the failure of a component at time t affects the performance of the working components at this age t. In this article, we study properties of the lifetimes of the coherent systems obtained using SOS. Specifically, we obtain a mixture representation based on the signature of the system. This representation is used to obtain stochastic comparisons. To get these comparisons, we obtain some ordering properties for the SOS, which in this context represent the lifetimes of k-out-of-n systems. In particular, we show that they are not necessarily hazard rate ordered.

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“…Generalized mixture representations based on minimal path sets and minimal cut sets were obtained by Esary and Proschan [7] (see also [2, p. 26]) in the case of independent components. Also, in this case, some comparison results were obtained in [14] and [21]. In the case of dependent heterogeneous components, representations and bounds for k-out-of-n systems (order statistics) were obtained in [24,Chapter 5], and comparisons between parallel and series systems were given in [17] and [18].…”

Section: )mentioning

confidence: 99%

Signature-Based Representations for the Reliability of Systems with Heterogeneous Components

Navarro

Samaniego

2011

J. Appl. Probab.

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Signature-based representations of the reliability functions of coherent systems with independent and identically distributed component lifetimes have proven very useful in studying the ageing characteristics of such systems and in comparing the performance of different systems under varied criteria. In this paper we consider extensions of these results to systems with heterogeneous components. New representation theorems are established for both the case of components with independent lifetimes and the case of component lifetimes under specific forms of dependence. These representations may be used to compare the performance of systems with homogeneous and heterogeneous components.

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Applications of average and projected systems to the study of coherent systems

Cited by 43 publications

References 21 publications

Limit of hazard rate function of coherent system with discrete life

Limit of hazard rate function of coherent system with discrete life

Coherent systems based on sequential order statistics

Signature-Based Representations for the Reliability of Systems with Heterogeneous Components

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