Stochastic comparisons of distorted distributions, coherent systems and mixtures with ordered components

Navarro, Jorge; Aguila, Yolanda del Aguila del

doi:10.1007/s00184-017-0619-y

Cited by 32 publications

(15 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The distortion function

\overset{true‾}{Q}

(or Q ) is an increasing continuous function such that

\overset{true‾}{Q} (0, \dots, 0) = 0

and

\overset{true‾}{Q} (1, \dots, 1) = 1

(ie, it is a continuous aggregation function). Ordering properties for generalized distorted distributions were given in Navarro et al () and Navarro and del Aguila (). We shall use these properties here to compare the different repair policies.…”

Section: Notation and Preliminary Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

“…Without loss of generality and by choosing an appropriate structure function, we can assume that the best component is X 1 , the second best is X 2 and so on. Thus, we can obtain the following theorem based on Propositions 2–4 of Navarro and del Aguila ().Theorem Let T r and T s be the lifetimes of a coherent system with the minimal repairs determined by the vectors r = ( r 1 , …, r n ) and s = ( s 1 , …, s n ) , respectively. Let

{\overset{Q}{true}}_{boldr}

and

{\overset{Q}{true}}_{bolds}

be the respective distortion functions in representation and let D = {( u 1 , …, u n ) ∈ (0, 1) n : u 1 ≥ … ≥ u n } .…”

Section: Minimal Repairs Allocation For Systems With Heterogeneous Comentioning

confidence: 93%

See 2 more Smart Citations

Stochastic comparisons of replacement policies in coherent systems under minimal repair

Arriaza

Navarro

Suárez‐Llorens

2018

Naval Research Logistics

Self Cite

View full text Add to dashboard Cite

In this paper, we study stochastic comparisons of the coherent systems obtained under different repair policies. We consider minimal repairs of the components, that is, a failed component is replaced by another component which is similar (ie, it has the same distribution) to the replaced one and with the same age. Under these assumptions, we study how to determine the best replacement policies. Two general methods are proposed, one for systems with identically distributed components and another one for systems with ordered (in different stochastic senses) components. Both methods can be applied to systems with independent or dependent components. We use these methods to determine the optimal repair policies in some particular cases. We pay special attention to series and parallel systems with independent or dependent components. An algorithm to find the optimal replacement policy (when it exists) is provided.

show abstract

“…The distortion function

\overset{true‾}{Q}

(or Q ) is an increasing continuous function such that

\overset{true‾}{Q} (0, \dots, 0) = 0

and

\overset{true‾}{Q} (1, \dots, 1) = 1

Section: Notation and Preliminary Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

{\overset{Q}{true}}_{boldr}

and

{\overset{Q}{true}}_{bolds}

be the respective distortion functions in representation and let D = {( u 1 , …, u n ) ∈ (0, 1) n : u 1 ≥ … ≥ u n } .…”

Section: Minimal Repairs Allocation For Systems With Heterogeneous Comentioning

confidence: 93%

See 1 more Smart Citation

Stochastic comparisons of replacement policies in coherent systems under minimal repair

Arriaza

Navarro

Suárez‐Llorens

2018

Naval Research Logistics

Self Cite

View full text Add to dashboard Cite

show abstract

“…In reliability, the study of the preservation of stochastic orders under the formation of coherent systems is an important topic that has attracted increasing attention (see Navarro et al, 16,17 Navarro and Gomis, 18 Navarro and del Aguila, 19 Arriaza et al, 20 Navarro and Sordo, 21 Navarro et al, 22 Li and Li, 23 and Navarro and Calì 24 ). In the case of ID components, this is equivalent, in view of (1) and (2), to study the preservation of stochastic orders under distortion functions.…”

Section: Introductionmentioning

confidence: 99%

Preservation of some stochastic orders by distortion functions with application to coherent systems with exchangeable components

Arriaza

Sordo

2020

Appl Stoch Models Bus & Ind

View full text Add to dashboard Cite

The preservation of stochastic orders by distortion functions has become a topic of increasing interest in the reliability analysis of coherent systems. The reason of this interest is that the reliability function of a coherent system with identically distributed components can be represented as a distortion function of the common reliability function of the components. In this framework, we study the preservation of the excess wealth order, the total time on test transform order, the decreasing mean residual live order, and the quantile mean inactivity time order by distortion functions. The results are applied to study the preservation of these stochastic orders under the formation of coherent systems with exchangeable components.

show abstract

“…Ordering properties for distorted distributions were obtained in Navarro et al, 8,9 Navarro and Gomis, 16 Navarro and del Águila 17 and Arriaza and Sordo 18 . Some of them are recalled here.…”

Section: Preliminariesmentioning

confidence: 75%

Connecting copula properties with reliability properties of coherent systems

Navarro

Durante

Sánchez

2020

Appl Stoch Models Bus & Ind

Self Cite

View full text Add to dashboard Cite

Summary We connect copula properties with stochastic comparisons between order statistics (k‐out‐of‐n systems) and coherent systems with dependent components. The copula dependence properties lead to marginal distribution‐free ordering properties between systems. Conversely, ordering properties of systems lead to properties (or new proofs of properties) for the baseline copulas. These relationships can be used to explain the meaning of mathematical properties and/or functional inequalities arising in the class of copulas. Some illustrative examples are provided including series and parallel systems with two or three components. The procedure introduced here can be applied to various system structures, even in high dimensions. In practice they can be used to determine various facets of dependency among the components of a system.

show abstract

Stochastic comparisons of distorted distributions, coherent systems and mixtures with ordered components

Cited by 32 publications

References 23 publications

Stochastic comparisons of replacement policies in coherent systems under minimal repair

Stochastic comparisons of replacement policies in coherent systems under minimal repair

Preservation of some stochastic orders by distortion functions with application to coherent systems with exchangeable components

Connecting copula properties with reliability properties of coherent systems

Contact Info

Product

Resources

About