Stochastic comparisons on conditional residual lifetime and inactivity time of coherent systems with exchangeable components

2019 ◽  
Vol 145 ◽  
pp. 327-337 ◽  
Author(s):  
Ebrahim Salehi ◽  
Mahdi Tavangar
Keyword(s):  
Residual Lifetime ◽  
Coherent Systems ◽  
Stochastic Comparisons ◽  
Inactivity Time

scholarly journals Dynamic Signatures of Coherent Systems Based on Sequential Order Statistics

2013 ◽  
Vol 50 (1) ◽  
pp. 272-287 ◽  
Author(s):  
M. Burkschat ◽  
J. Navarro
Keyword(s):  
Order Statistics ◽  
Failure Time ◽  
Residual Lifetime ◽  
Coherent Systems ◽  
Sequential Order ◽  
Stochastic Comparisons ◽  
Additional Information ◽  
Structured Systems ◽  
Sequential Order Statistics ◽  
Inactivity Time

Sequential order statistics can be used to describe the ordered lifetimes of components in a system, where the failure of a component may affect the performance of remaining components. In this paper mixture representations of the residual lifetime and the inactivity time of systems with such failure-dependent components are considered. Stochastic comparisons of differently structured systems are obtained and properties of the weights in the mixture representations are examined. Furthermore, corresponding representations of the residual lifetime and the inactivity time of a system given the additional information about a previous failure time are derived.

Dynamic Signatures of Coherent Systems Based on Sequential Order Statistics

2013 ◽  
Vol 50 (01) ◽  
pp. 272-287 ◽  
Author(s):  
M. Burkschat ◽  
J. Navarro
Keyword(s):  
Order Statistics ◽  
Failure Time ◽  
Residual Lifetime ◽  
Coherent Systems ◽  
Sequential Order ◽  
Stochastic Comparisons ◽  
Additional Information ◽  
Structured Systems ◽  
Sequential Order Statistics ◽  
Inactivity Time

Sequential order statistics can be used to describe the ordered lifetimes of components in a system, where the failure of a component may affect the performance of remaining components. In this paper mixture representations of the residual lifetime and the inactivity time of systems with such failure-dependent components are considered. Stochastic comparisons of differently structured systems are obtained and properties of the weights in the mixture representations are examined. Furthermore, corresponding representations of the residual lifetime and the inactivity time of a system given the additional information about a previous failure time are derived.

scholarly journals On the Conditional Residual Life and Inactivity Time of Coherent Systems

2014 ◽  
Vol 51 (4) ◽  
pp. 990-998 ◽  
Author(s):  
A. Parvardeh ◽  
N. Balakrishnan
Keyword(s):  
Residual Life ◽  
Coherent System ◽  
Coherent Systems ◽  
Stochastic Comparisons ◽  
Distributed Components ◽  
Inactivity Time ◽  
Independent And Identically Distributed

In this paper we derive mixture representations for the reliability functions of the conditional residual life and inactivity time of a coherent system with n independent and identically distributed components. Based on these mixture representations we carry out stochastic comparisons on the conditional residual life, and the inactivity time of two coherent systems with independent and identical components.

On the Conditional Residual Life and Inactivity Time of Coherent Systems

2014 ◽  
Vol 51 (04) ◽  
pp. 990-998
Author(s):  
A. Parvardeh ◽  
N. Balakrishnan
Keyword(s):  
Residual Life ◽  
Coherent System ◽  
Coherent Systems ◽  
Stochastic Comparisons ◽  
Distributed Components ◽  
Inactivity Time ◽  
Independent And Identically Distributed

In this paper we derive mixture representations for the reliability functions of the conditional residual life and inactivity time of a coherent system with n independent and identically distributed components. Based on these mixture representations we carry out stochastic comparisons on the conditional residual life, and the inactivity time of two coherent systems with independent and identical components.

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.

Stochastic Comparisons Between Coherent Systems with Active Redundancies Under Proportional Hazards and Reversed Hazards Models

2020 ◽  
Vol 28 (01) ◽  
pp. 2150007
Author(s):  
Maryam Kelkinnama
Keyword(s):  
Proportional Hazards ◽  
Sufficient Conditions ◽  
System Level ◽  
Coherent Systems ◽  
Stochastic Comparisons ◽  
Component Level ◽  
Lifetime Distributions ◽  
Hazards Model ◽  
System Improvement

This paper is concerned with the problem of stochastic comparisons between the lifetimes of two coherent systems with active redundancy. For this purpose, we consider both the active redundancy at the system level and the redundancy at the component level. We assume that the original components are identically distributed and possibly dependent. It is also assumed that for each component, there are [Formula: see text] redundant components with possibly different lifetime distributions which follow the proportional hazards (reversed hazards) model. Under some conditions on the domination function of the system, we compare the lifetimes of the systems based on majorization orders between the parameter vectors of the proportionality of the component lifetimes. We also give sufficient conditions under which adding more redundant components imply the system improvement.

scholarly journals Mixture Representations of Inactivity Times of Conditional Coherent Systems and their Applications

2010 ◽  
Vol 47 (03) ◽  
pp. 876-885 ◽  
Author(s):  
Zhengcheng Zhang
Keyword(s):  
Order Statistics ◽  
Reliability Function ◽  
Coherent System ◽  
Coherent Systems ◽  
Distributed Components ◽  
Inactivity Time ◽  
Independent And Identically Distributed

In this paper we obtain several mixture representations of the reliability function of the inactivity time of a coherent system under the condition that the system has failed at time t (> 0) in terms of the reliability functions of inactivity times of order statistics. Some ordering properties of the inactivity times of coherent systems with independent and identically distributed components are obtained, based on the stochastically ordered coefficient vectors between systems.

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