Optimal allocation of components in parallel–series and series–parallel systems

This paper shows how majorization and Schur-convex functions can be used to solve the problem of optimal allocation of components to parallel-series and series-parallel systems to maximize the reliability of the system. For parallel-series systems the optimal allocation is completely described and depends only on the ordering of component reliabilities. For series-parallel systems, we describe a partial ordering among allocations that can lead to the optimal allocation. Finally, we describe how these problems can be cast as integer linear programming problems and thus the results obtained in this paper show that when some linear integer programming problems are recast in a different way and the techniques of Schur functions are used, complete solutions can be obtained in some instances and better insight in others.

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Optimal allocation of components in parallel–series and series–parallel systems

Journal of Applied Probability ◽

10.1017/s002190020011191x ◽

1986 ◽

Vol 23 (03) ◽

pp. 770-777

Author(s):

Emad El-Neweihi ◽

Frank Proschan ◽

Jayaram Sethuraman

Keyword(s):

Optimal Allocation ◽

Schur Functions ◽

Parallel Systems ◽

Partial Ordering ◽

Linear Integer Programming ◽

Linear Programming Problems ◽

Schur Convex ◽

Integer Programming Problems ◽

Series Systems ◽

Parallel Series

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Optimal allocation of a coherent system with statistical dependent subsystems

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964821000437 ◽

2021 ◽

pp. 1-20

Author(s):

Bin Lu ◽

Jiandong Zhang ◽

Rongfang Yan

Keyword(s):

Hazard Rate ◽

Optimal Allocation ◽

Stochastic Order ◽

Sufficient Conditions ◽

Parallel Systems ◽

Coherent System ◽

Allocation Policy ◽

Usual Stochastic Order ◽

Series Systems ◽

Parallel Series

Abstract This paper studies the optimal allocation policy of a coherent system with independent heterogeneous components and dependent subsystems, the systems are assumed to consist of two groups of components whose lifetimes follow proportional hazard (PH) or proportional reversed hazard (PRH) models. We investigate the optimal allocation strategy by finding out the number $k$ of components coming from Group A in the up-series system. First, some sufficient conditions are provided in the sense of the usual stochastic order to compare the lifetimes of two-parallel–series systems with dependent subsystems, and we obtain the hazard rate and reversed hazard rate orders when two subsystems have independent lifetimes. Second, similar results are also obtained for two-series–parallel systems under certain conditions. Finally, we generalize the corresponding results to parallel–series and series–parallel systems with multiple subsystems in the viewpoint of the minimal path and the minimal cut sets, respectively. Some numerical examples are presented to illustrate the theoretical findings.

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Active Redundancy Allocation in Coherent Systems

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964800000899 ◽

1988 ◽

Vol 2 (3) ◽

pp. 343-353 ◽

Cited By ~ 62

Author(s):

Philip J. Boland ◽

Emad El Neweihi ◽

Frank Proschan

Keyword(s):

Parallel Systems ◽

Coherent System ◽

Coherent Systems ◽

Redundancy Allocation ◽

Structural Importance ◽

Component Importance ◽

Series Systems ◽

Made In ◽

Parallel Series

We introduce in this paper a new measure of component importance, called redundancy importance, in coherent systems. It is a measure of importance for the situation in which an active redundancy is to be made in a coherent system. This measure of component importance is compared with both the (Birnbaum) reliability importance and the structural importance of a component in a coherent system. Various models of component redundancy are studied, with particular reference to k/out / of / n systems, parallel-series systems, and series-parallel systems.

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ON VARIABILITY OF SERIES AND PARALLEL SYSTEMS WITH HETEROGENEOUS COMPONENTS

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964819000263 ◽

2019 ◽

Vol 34 (4) ◽

pp. 626-645

Author(s):

Yiying Zhang ◽

Weiyong Ding ◽

Peng Zhao

Keyword(s):

Sufficient Conditions ◽

Parallel Systems ◽

Hazard Rates ◽

Series System ◽

Proportional Hazard ◽

Lifetime Distributions ◽

Scale Parameters ◽

Convex Transform Order ◽

Series Systems ◽

Parallel Series

AbstractThis paper studies the variability of both series and parallel systems comprised of heterogeneous (and dependent) components. Sufficient conditions are established for the star and dispersive orderings between the lifetimes of parallel [series] systems consisting of dependent components having multiple-outlier proportional hazard rates and Archimedean [Archimedean survival] copulas. We also prove that, without any restriction on the scale parameters, the lifetime of a parallel or series system with independent heterogeneous scaled components is larger than that with independent homogeneous scaled components in the sense of the convex transform order. These results generalize some corresponding ones in the literature to the case of dependent scenarios or general settings of components lifetime distributions.

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Optimal Allocation of Components in k-out-of-R Parallel Modules Systems

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964800003521 ◽

1994 ◽

Vol 8 (3) ◽

pp. 435-441 ◽

Cited By ~ 1

Author(s):

Fan Chin Meng

Keyword(s):

System Reliability ◽

Optimal Allocation ◽

Parallel Systems ◽

Coherent Systems ◽

Special Case

In this note using the notion of node criticality in Boland, Proschan, and Tong [2] and modular decompositions of coherent systems, we obtain algorithms and guidelines for allocating components in a k-out-of-R parallel modules system to maximize the system reliability. An illustrative example is given to compare a special case of our results with the previous result for series-parallel systems due to El-Neweihi, Proschan, and Sethuraman [5].

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Optimal allocation of resources to nodes of parallel and series systems

Advances in Applied Probability ◽

10.2307/1427718 ◽

1992 ◽

Vol 24 (4) ◽

pp. 894-914 ◽

Cited By ~ 54

Author(s):

Moshe Shaked ◽

J. George Shanthikumar

Keyword(s):

Optimal Allocation ◽

Allocation Of Resources ◽

Series Systems ◽

Total Resource

In this paper we consider parallel and series systems, the components of which can be ‘improved'. The ‘improvement' consists of supplying the components with cold or hot standby spares or by allotting to them fixed budgets for minimal repairs. A fixed total resource of spares or minimal repairs is available. We find the optimal allocation of the resource items in several commonly encountered settings.

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