Optimal Allocation of Active Redundancies to <i>k</i>-out-of-<i>n</i> Systems with Heterogeneous Components

Li, Xiaohu; Ding, Weiyong

doi:10.1239/jap/1269610829

Cited by 47 publications

(18 citation statements)

References 10 publications

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“…A relevant problem in reliability theory is to determine the optimal replacement policy (under different criteria) for the components in a given system structure. Many results have been obtained under the assumption of independent components (see, eg, Barlow & Proschan, 1975;Belzunce, Martínez-Riquelme, & Ruiz, 2018;Boland & El-Neweihi, 1995;Chahkandi et al, 2016;Boland, El-Neweihi, & Proschan, 1992;Li & Ding, 2010;Natvig, 2011;Shaked & Shanthikumar, 1992). Different assumptions have been made for the redundant components.…”

Section: Introductionmentioning

confidence: 99%

Stochastic comparisons of replacement policies in coherent systems under minimal repair

Arriaza

Navarro

Suárez‐Llorens

2018

Naval Research Logistics

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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.

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Section: Introductionmentioning

confidence: 99%

Stochastic comparisons of replacement policies in coherent systems under minimal repair

Arriaza

Navarro

Suárez‐Llorens

2018

Naval Research Logistics

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“…Naturally, one may wonder how close the two allocation numbers should be. According to Li and Ding (), for

k

‐out‐of‐

n

systems with independent base component lifetimes

X_{1} \geq_{st} \dots \geq_{st} X_{n}

and i.i.d. redundancy component lifetimes

Y_{i} \geq_{st} X_{1}

i = 1, \dots, m

, if all redundancy components are assigned to two base components

X_{k}

and

X_{ℓ}

, then the strategy

(r_{k}, r_{ℓ})

such that

r_{ℓ} - 1 \leq r_{k} \leq r_{ℓ}

is the optimal one.…”

Section: Optimal Allocation Strategy For Symmetric Systemsmentioning

confidence: 99%

On matched active redundancy allocation for coherent systems with statistically dependent component lifetimes

Fang

2017

Naval Research Logistics

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This study addresses the allocation of matched active redundancy components to coherent systems with base components having statistically dependent lifetimes. We consider base component lifetimes and redundancy component lifetimes which are both stochastic arrangement monotone with respect to a pair of components given the lifetimes of the other components. In this context, allocating a more reliable redundancy component to the weaker base component is shown to incur a stochastically larger system lifetime. Numerical examples are presented as an illustration of the theoretical results.

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“…Recently, Li and Ding [9] proved in the following result that more redundancies should be allocated to the component with stochastically smaller lifetime under the framework that redundancies are i.i.d. and the working components are independent.…”

Section: Multiple Active Redundanciesmentioning

confidence: 99%

“…active redundancies allocated to a series system with n independent stochastically ordered components, Misra et al showed that the lifetime of the resulting series system has a survival function Schur‐concave with respect to r in

({}, (r_{1} MathClass-punc, MathClass-rel\dots MathClass-punc, r_{n}) MathClass-punc: r_{1} ⩾ MathClass-rel\dots ⩾ r_{n} MathClass-punc, r_{1} MathClass-bin+ MathClass-rel\dots MathClass-bin+ r_{n} MathClass-rel= m MathClass-punc, r_{i} MathClass-rel\in N MathClass-punc, i MathClass-rel= 1 MathClass-punc, MathClass-rel\dots MathClass-punc, n)

. Afterward, Li and Ding further investigated the allocation of m active redundancies and deduced that allocating more redundancies to the weaker component will stochastically increase the system's lifetime.…”

Section: Introductionmentioning

confidence: 99%

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On allocating redundancies to k‐out‐of‐ n reliability systems

You

2014

Appl Stoch Models Bus & Ind

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For two components in series and one redundancy with their lifetimes following the proportional hazard models, we build the likelihood ratio order and the hazard rate order for lifetimes of the redundant systems. Also, for k‐out‐of‐ n system with components’ lifetimes having the arrangement increasing joint density and the redundancies having identically distributed lifetimes, allocating more redundancies to weaker components is shown to help improve the system's reliability. Copyright © 2014 John Wiley & Sons, Ltd.

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Optimal Allocation of Active Redundancies to k-out-of-n Systems with Heterogeneous Components

Cited by 47 publications

References 10 publications

Stochastic comparisons of replacement policies in coherent systems under minimal repair

Stochastic comparisons of replacement policies in coherent systems under minimal repair

On matched active redundancy allocation for coherent systems with statistically dependent component lifetimes

On allocating redundancies to k‐out‐of‐ n reliability systems

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