Optimal allocation of a coherent system with statistical dependent subsystems

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.

COMPARISONS OF SAMPLE RANGES ARISING FROM MULTIPLE-OUTLIER MODELS: IN MEMORY OF MOSHE SHAKED

2017 ◽  
Vol 33 (1) ◽  
pp. 28-49
Author(s):  
Narayanaswamy Balakrishnan ◽  
Jianbin Chen ◽  
Yiying Zhang ◽  
Peng Zhao
Keyword(s):  
Hazard Rate ◽  
Stochastic Order ◽  
Sufficient Conditions ◽  
Hazard Rates ◽  
Proportional Hazard ◽  
Stochastic Comparisons ◽  
Hazard Rate Order ◽  
Numerical Examples ◽  
Reversed Hazard Rate ◽  
Usual Stochastic Order

In this paper, we discuss the ordering properties of sample ranges arising from multiple-outlier exponential and proportional hazard rate (PHR) models. The purpose of this paper is twofold. First, sufficient conditions on the parameter vectors are provided for the reversed hazard rate order and the usual stochastic order between the sample ranges arising from multiple-outlier exponential models with common sample size. Next, stochastic comparisons are separately carried out for sample ranges arising from multiple-outlier exponential and PHR models with different sample sizes as well as different hazard rates. Some numerical examples are also presented to illustrate the results established here.

Active Redundancy Allocation in Coherent Systems

1988 ◽  
Vol 2 (3) ◽  
pp. 343-353 ◽  
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.

ON VARIABILITY OF SERIES AND PARALLEL SYSTEMS WITH HETEROGENEOUS COMPONENTS

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.

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

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

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.

scholarly journals Comparisons of Parallel Systems with Components Having Proportional Reversed Hazard Rates and Starting Devices

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 856
Author(s):  
Narayanaswamy Balakrishnan ◽  
Ghobad Barmalzan ◽  
Sajad Kosari
Keyword(s):  
Hazard Rate ◽  
Stochastic Order ◽  
Parallel Systems ◽  
Hazard Rates ◽  
Stochastic Comparisons ◽  
Reversed Hazard Rate ◽  
Usual Stochastic Order ◽  
Distributed Components

In this paper, we consider stochastic comparisons of parallel systems with proportional reversed hazard rate (PRHR) distributed components equipped with starting devices. By considering parallel systems with two components that PRHR and starting devices, we prove the hazard rate and reversed hazard rate orders. These results are then generalized for such parallel systems with n components in terms of usual stochastic order. The establish results are illustrated with some examples.

scholarly journals Stochastic Comparisons of Parallel and Series Systems with Type II Half Logistic-Resilience Scale Components

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 470 ◽  
Author(s):  
Junrui Wang ◽  
Rongfang Yan ◽  
Bin Lu
Keyword(s):  
Stochastic Order ◽  
Distribution Functions ◽  
Series System ◽  
Type Ii ◽  
Stochastic Comparisons ◽  
Hazard Rate Order ◽  
Usual Stochastic Order ◽  
Resilience Scale ◽  
Series Systems ◽  
Parallel Series

This paper deals with stochastic comparisons of two parallel (series) systems with Type II half logistic-resilience scale (TIIHL-RS) distribution components with different baseline distribution functions. Under the conditions of interdependency and independency, the research shows that the system performance is better (worse) with the stronger component heterogeneity in the parallel (series) system under the usual stochastic order and the (reversed) hazard rate order.

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

1986 ◽  
Vol 23 (3) ◽  
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

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.

Optimal allocation of relevations in coherent systems

2021 ◽  
Vol 58 (4) ◽  
pp. 1152-1169
Author(s):  
Rongfang Yan ◽  
Jiandong Zhang ◽  
Yiying Zhang
Keyword(s):  
Optimal Allocation ◽  
Necessary Conditions ◽  
Stochastic Order ◽  
Coherent Systems ◽  
Stochastic Comparisons ◽  
Hazard Rate Order ◽  
Usual Stochastic Order ◽  
Special Cases ◽  
Sufficient And Necessary Conditions ◽  
Allocation Strategies

AbstractIn this paper we study the allocation problem of relevations in coherent systems. The optimal allocation strategies are obtained by implementing stochastic comparisons of different policies according to the usual stochastic order and the hazard rate order. As special cases of relevations, the load-sharing and minimal repair policies are further investigated. Sufficient (and necessary) conditions are established for various stochastic orderings. Numerical examples are also presented as illustrations.

scholarly journals Stochastic Order Relations Among Parallel Systems from Weibull Distributions

2015 ◽  
Vol 52 (01) ◽  
pp. 102-116 ◽  
Author(s):  
Nuria Torrado ◽  
Subhash C. Kochar
Keyword(s):  
Likelihood Ratio ◽  
Hazard Rate ◽  
Stochastic Order ◽  
Random Variables ◽  
Parallel Systems ◽  
Parallel System ◽  
Weibull Distributions ◽  
Scale Parameters ◽  
Order Relations ◽  
Stochastic Order Relations

Let X λ1 , X λ2 , …, X λ n be independent Weibull random variables with X λ i ∼ W(α, λ i ), where λ i > 0 for i = 1, …, n. Let X n:n λ denote the lifetime of the parallel system formed from X λ1 , X λ2 , …, X λ n . We investigate the effect of the changes in the scale parameters (λ1, …, λ n ) on the magnitude of X n:n λ according to reverse hazard rate and likelihood ratio orderings.

ON RELATIVE AGING COMPARISONS OF COHERENT SYSTEMS WITH IDENTICALLY DISTRIBUTED COMPONENTS

2020 ◽  
pp. 1-15 ◽  
Author(s):  
Nil Kamal Hazra ◽  
Neeraj Misra
Keyword(s):  
Hazard Rate ◽  
Sufficient Conditions ◽  
Stochastic Orders ◽  
Coherent System ◽  
Coherent Systems ◽  
Cumulative Hazard ◽  
Numerical Examples ◽  
Distributed Components ◽  
Rate Functions ◽  
Important Notion

The relative aging is an important notion which is useful to measure how a system ages relative to another one. Among the existing stochastic orders, there are two important orders describing the relative aging of two systems, namely, aging faster orders in the cumulative hazard and the cumulative reversed hazard rate functions. In this paper, we give some sufficient conditions under which one coherent system ages faster than another one with respect to the aforementioned stochastic orders. Further, we show that the proposed sufficient conditions are satisfied for k-out-of-n systems. Moreover, some numerical examples are given to illustrate the applications of proposed results.

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