Reliability optimization in series-parallel and parallel-series systems subject to random shocks

2021 ◽  
pp. 1748006X2110126
Author(s):  
Xiaoliang Ling ◽  
Yazhou Zhang ◽  
Yu Gao
Keyword(s):  
Optimization Problems ◽  
Reliability Function ◽  
Reliability Optimization ◽  
Series System ◽  
Nonhomogeneous Poisson Processes ◽  
Majorization Order ◽  
In Series ◽  
Random Shocks ◽  
Series Systems ◽  
Parallel Series

Consider a series-parallel (parallel-series) system composed of [Formula: see text] subsystems subject to [Formula: see text] independent stochastically identical nonhomogeneous Poisson processes, its reliability optimization problems are analysed in this paper. The reliability function of the series-parallel (parallel-series) system is presented. We study the optimal subsystems grouping policy to maximize the system reliability. It is shown that the series-parallel (parallel-series) system is more reliable (unreliable) when more subsystems share a common combined shock process. Different allocation policies of components are compared in terms of majorization order. Some examples are given to illustrate the results.

ON OPTIMAL HETEROGENEOUS COMPONENTS GROUPING IN SERIES-PARALLEL AND PARALLEL-SERIES SYSTEMS

2018 ◽  
Vol 33 (4) ◽  
pp. 564-578 ◽  
Author(s):  
Xiaoliang Ling ◽  
Yinzhao Wei ◽  
Ping Li
Keyword(s):  
System Reliability ◽  
Heterogeneous Population ◽  
The Other ◽  
Series System ◽  
In Series ◽  
Selection Probabilities ◽  
The Impact ◽  
Series Systems ◽  
Parallel Series

In this paper, we consider optimal components grouping in series–parallel and parallel–series systems composed of k subsystems. All components in each subsystem are drawn from a heterogeneous population consisting of m different subpopulations. Firstly, we show that when one allocation vector is majorized by another one, then the series–parallel (parallel–series) system corresponding to the first (second) vector is more reliable than that of the other. Secondly, we study the impact of changes in the number of subsystems on the system reliability. Finally, we study the influence of the selection probabilities of subpopulations on the system reliability.

COMBINED SERIES AND PARALLEL SYSTEMS SUBJECT TO INDIVIDUAL VERSUS OVERARCHING DEFENSE AND ATTACK

2013 ◽  
Vol 30 (02) ◽  
pp. 1250056 ◽  
Author(s):  
KJELL HAUSKEN
Keyword(s):  
Parallel Systems ◽  
Series System ◽  
Number Of Components ◽  
Unit Costs ◽  
Special Cases ◽  
In Series ◽  
Individual Protection ◽  
Overarching Protection ◽  
Series Systems ◽  
Analytical Expressions

A system of components can be in series, parallel, or combined series/parallel. The components and system are protected individually and overarchingly by a defender, and attacked individually and overarchingly by an attacker. Both layers of protection have to be breached for an attack to be successful. Each component, and the system as a whole, have vulnerabilities determined by individual and overarching protection and attack. The agents choose their effort variables simultaneously and independently to maximize their utilities. Each component and the system have unit costs of protection and attack, and a contest intensity. We show for both the parallel and series systems that the defender always prefers overarching and individual protection and attack, while the attacker always prefers individual protection and attack. Analytical expressions are developed for the agents' effort variables, each individual component's vulnerability, and the system vulnerability. The expenditure ratio, between individual protection and attack, and overarching protection and attack, is shown to increase in the number of components for the parallel system, and decrease in the number of components for the series system. Special cases are considered and interpreted. Comparisons are made with only individual protection and attack. The model is applicable to determine how the defender and attacker should strike the balance between choosing efforts to protect and attack components individually versus overarchingly.

ON COMPONENT FAILURES' DEPENDENCY INFLUENCE ON SYSTEM'S LIFETIME

2007 ◽  
Vol 14 (06) ◽  
pp. 517-535 ◽  
Author(s):  
AGNIESZKA BLOKUS-ROSZKOWSKA
Keyword(s):  
Reliability Function ◽  
Reliability Evaluation ◽  
Transportation System ◽  
Asymptotic Approach ◽  
Reliability Characteristics ◽  
Component Failures ◽  
Series Systems ◽  
Theoretical Results ◽  
Parallel Series

In the paper the results of the reliability investigation of multi-state homogeneous parallel-series systems with independent and dependent components are presented. The multi-state reliability functions of such systems and other reliability characteristics in both cases are determined under the assumption that their components have exponential reliability function. Moreover the asymptotic approach to the reliability evaluation of these systems is also presented and the classes of limit reliability functions for the considered systems in both cases are fixed. Finally, the presented theoretical results are applied to the reliability evaluation of the shipyard rope transportation system. The comparison of the multi-state exact and limit reliability functions of the considered transportation system under the assumption that its components are independent and under the assumption that its components have failure dependency is performed and illustrated graphically.

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.

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.

scholarly journals Use of copula functions for the reliability of series systems

2015 ◽  
Vol 32 (6) ◽  
pp. 617-634 ◽  
Author(s):  
Jorge Alberto Achcar ◽  
Fernando Antonio Moala
Keyword(s):  
Simulated Data ◽  
Reliability Function ◽  
Good Alternative ◽  
Bivariate Distribution ◽  
Parametric Models ◽  
Dependence Structure ◽  
Series System ◽  
Copula Functions ◽  
Content Type ◽  
Series Systems

Purpose – The purpose of this paper is to provide a new method to estimate the reliability of series system by using copula functions. This problem is of great interest in industrial and engineering applications. Design/methodology/approach – The authors introduce copula functions and consider a Bayesian analysis for the proposed models with application to the simulated data. Findings – The use of copula functions for modeling the bivariate distribution could be a good alternative to estimate the reliability of a two components series system. From the results of this study, the authors observe that they get accurate Bayesian inferences for the reliability function considering large samples sizes. The Bayesian parametric models proposed also allow the assessment of system reliability for multicomponent systems simultaneously. Originality/value – Usually, the studies of systems reliability engineering assume independence among the component lifetimes. In the approach the authors consider a dependence structure. Using standard classical inference methods based on asymptotical normality of the maximum likelihood estimators for the parameters the authors could have great computational difficulties and possibly, not accurate inference results, which there is not found in the approach.

RELIABILITY ANALYSIS OF LARGE SYSTEMS WITH DEPENDENT COMPONENTS

2006 ◽  
Vol 13 (01) ◽  
pp. 1-14 ◽  
Author(s):  
AGNIESZKA BLOKUS
Keyword(s):  
Reliability Analysis ◽  
Reliability Evaluation ◽  
Parallel System ◽  
Series System ◽  
Dependent Failures ◽  
Large Systems ◽  
Series Systems ◽  
Parallel Series

Dependent failures of components in parallel and parallel-series systems are defined. Reliability functions of parallel and parallel-series systems composed of dependent components and their limit forms are determined. The results are applied to the reliability evaluation of an exemplary parallel system and to the shipyard rope transportation parallel-series system.

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