On Maximum Reliability Problem in Parallel-Series Systems with Two Failure Modes

2000 ◽  
pp. 148-159
Author(s):  
Vladimir Kirilyuk
Keyword(s):  
Failure Modes ◽  
Reliability Problem ◽  
Series Systems ◽  
Maximum Reliability ◽  
Parallel Series

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.

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.

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.

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