Limit of hazard rate function of coherent system with discrete life

Mi, Jie

doi:10.1002/asmb.863

Cited by 2 publications

(2 citation statements)

References 19 publications

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“…Moreover, they obtain distribution‐free ordering properties used to compare systems having different numbers of exchangeable components. Other ordering properties and bounds for systems were obtained in . Unfortunately, Samaniego's representation does not necessarily hold when the components are not exchangeable (see Example 5.1 in ).…”

Section: Introductionmentioning

confidence: 99%

Stochastic ordering properties for systems with dependent identically distributed components

Navarro

Aguila

Sordo

et al. 2012

Appl Stoch Models Bus & Ind

115

106

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In this paper, we obtain ordering properties for coherent systems with possibly dependent identically distributed components. These results are based on a representation of the system reliability function as a distorted function of the common component reliability function. So, the results included in this paper can also be applied to general distorted distributions. The main advantage of these results is that they are distribution-free with respect to the common component distribution. Moreover, they can be applied to systems with component lifetimes having a non-exchangeable joint distribution. Appl. Stochastic ModelsBus. Ind. 2013, 29 264-278 J. NAVARRO ET AL.The rest of the paper is organized as follows. In Section 2, we give the main results of the paper with the general ordering results for distorted distributions and coherent systems with ID components. Specifically, we study properties of the usual stochastic order, hazard rate order, the reversed hazard rate order, the likelihood ratio order, the increasing convex order, the total time on test transform order, and the excess wealth order. In Section 3, we give some examples to show how to apply our general results to specific systems. These examples include systems with IID components and systems with dependent ID components. In Section 4, we give some conclusions and open questions for future research.Throughout the paper, we use the terms increasing and decreasing in a wide sense, that is, a function g is increasing (decreasing) if g.x/ 6 g.y/.>/ for all x 6 y. Whenever we consider an expectation (or a conditional random variable), we assume that it exists. The main resultsLet us consider a coherent system with lifetime T D .X 1 ; : : : ; X n / based on possibly dependent components with lifetimes X 1 ; : : : ; X n , where is the structure function (see [29], Chapter 1). Let us assume that X 1 ; : : : ; X n are identically distributed (ID) with a common reliability function F .t/ D Pr.X i > t/ for i D 1; : : : ; n. The component lifetimes X 1 ; : : : ; X n can be dependent, and this dependence will be represented by the joint reliability (or survival) function of .X

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Section: Introductionmentioning

confidence: 99%

Stochastic ordering properties for systems with dependent identically distributed components

Navarro

Aguila

Sordo

et al. 2012

Appl Stoch Models Bus & Ind

115

106

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show abstract

“…Recently Mi [13] considered the situation in which the components of the system had discrete lifetimes and investigated some of aging properties of the system. The aim of the present paper is to study the MRL of ( ) …”

Section: T T T T T R K K Nmentioning

confidence: 99%

The Mean Residual Lifetime of (n － k + 1)-out-of-n Systems in Discrete Setting

Siahboomi¹

2014

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In real life, there are situations in which the lifetime of the components of a technical system (and hence the lifetime of the system) is discrete. In this paper, we study the residual life, a (n − k + 1)-out-of-n system under the assumptions that the components of the system are independent identically distributed with common discrete distribution function F. We define the mean residual lifetime (MRL) of the system and under different scenarios investigate several aging and stochastic properties of MRL.

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Limit of hazard rate function of coherent system with discrete life

Cited by 2 publications

References 19 publications

Stochastic ordering properties for systems with dependent identically distributed components

Stochastic ordering properties for systems with dependent identically distributed components

The Mean Residual Lifetime of (<i>n</i> － <i> k</i> + 1)-out-of-<i>n</i> Systems in Discrete Setting

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Limit of hazard rate function of coherent system with discrete life

Cited by 2 publications

References 19 publications

Stochastic ordering properties for systems with dependent identically distributed components

Stochastic ordering properties for systems with dependent identically distributed components

The Mean Residual Lifetime of (&lt;i&gt;n&lt;/i&gt; － &lt;i&gt; k&lt;/i&gt; + 1)-out-of-&lt;i&gt;n&lt;/i&gt; Systems in Discrete Setting

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The Mean Residual Lifetime of (<i>n</i> － <i> k</i> + 1)-out-of-<i>n</i> Systems in Discrete Setting