scholarly journals ON STOCHASTIC COMPARISONS FOR LOAD-SHARING SERIES AND PARALLEL SYSTEMS

2016 ◽  
Vol 31 (3) ◽  
pp. 311-329 ◽  
Author(s):  
Maxim Finkelstein ◽  
Nil Kamal Hazra
Keyword(s):  
Parallel Systems ◽  
Load Sharing ◽  
Parallel System ◽  
Cumulative Exposure ◽  
Exposure Model ◽  
Stochastic Comparisons ◽  
Cumulative Exposure Model ◽  
Redundant Component ◽  
Allocation Strategies ◽  
Additional Assumptions

We study the allocation strategies for redundant components in the load-sharing series/parallel systems. We show that under the specified assumptions, the allocation of a redundant component to the stochastically weakest (strongest) component of a series (parallel) system is the best strategy to achieve its maximal reliability. The results have been studied under cumulative exposure model and for a general scenario as well. They have a clear intuitive meaning; however, the corresponding additional assumptions are not obvious, which can be seen from the proofs of our theorems.

Stochastic comparisons of series and parallel systems with independent heterogeneous Gumbel and truncated Gumbel components

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Fatih Kızılaslan
Keyword(s):  
Likelihood Ratio ◽  
Hazard Rate ◽  
Design Methodology ◽  
Parallel Systems ◽  
Parallel System ◽  
Series System ◽  
Stochastic Comparisons ◽  
Content Type ◽  
Reversed Hazard Rate ◽  
The Relationship

PurposeThe purpose of this paper is to investigate the stochastic comparisons of the parallel system with independent heterogeneous Gumbel components and series and parallel systems with independent heterogeneous truncated Gumbel components in terms of various stochastic orderings.Design/methodology/approachThe obtained results in this paper are obtained by using the vector majorization methods and results. First, the components of series and parallel systems are heterogeneous and having Gumbel or truncated Gumbel distributions. Second, multiple-outlier truncated Gumbel models are discussed for these systems. Then, the relationship between the systems having Gumbel components and Weibull components are considered. Finally, Monte Carlo simulations are performed to illustrate some obtained results.FindingsThe reversed hazard rate and likelihood ratio orderings are obtained for the parallel system of Gumbel components. Using these results, similar new results are derived for the series system of Weibull components. Stochastic comparisons for the series and parallel systems having truncated Gumbel components are established in terms of hazard rate, likelihood ratio and reversed hazard rate orderings. Some new results are also derived for the series and parallel systems of upper-truncated Weibull components.Originality/valueTo the best of our knowledge thus far, stochastic comparisons of series and parallel systems with Gumbel or truncated Gumble components have not been considered in the literature. Moreover, new results for Weibull and upper-truncated Weibull components are presented based on Gumbel case results.

Reliability analysis of load-sharing parallel systems considering equivalent strength degradation

2020 ◽  
pp. 1748006X2096842
Author(s):  
Xinshui Yu ◽  
Tianxiang Yu ◽  
Kunling Song ◽  
Bifeng Song
Keyword(s):  
Parallel Systems ◽  
Original System ◽  
Load Sharing ◽  
Degradation Process ◽  
Strength Degradation ◽  
Parallel System ◽  
Failure Behavior ◽  
Initial Strength ◽  
Reliability Method ◽  
Equivalent Strength

In this paper, a new reliability method for load-sharing parallel systems with dependent components that share the workload equally before and after some components have failed is studied. In the working process of a load-sharing parallel system, after the failure of some components, the surviving components share the original system workload with higher components loads. The states of all the components are dependent. The failure behavior of a component impacts the strength degradation process of the remaining working components. For a load-sharing parallel system, one component works the whole system works, which means the component with the largest initial strength works, the whole system works. Firstly, we use the equivalent strength degradation theory to get the remaining strength of the component with the largest initial strength after some components fail. Then, the stress-strength interference model will be used to calculate the reliability after some components fail. Finally, the proposed method is illustrated by a numerical example and verified by the Monte Carlo simulation method.

scholarly journals Reliability Properties of Residual Life Time and Inactivity Time of Series and Parallel System

2012 ◽  
Vol 8 (1) ◽  
pp. 5-16 ◽  
Author(s):  
Nitin Gupta ◽  
Neeraj Gandotra ◽  
Rakesh Bajaj
Keyword(s):  
Residual Life ◽  
Sufficient Conditions ◽  
Parallel Systems ◽  
Life Time ◽  
Parallel System ◽  
Time Data ◽  
Stochastic Comparisons ◽  
Aging Properties ◽  
Inactivity Time ◽  
In Series

Reliability Properties of Residual Life Time and Inactivity Time of Series and Parallel SystemThe concepts of residual life time and inactivity time are extensively used in reliability theory for modeling life time data. In this paper we prove some new results on stochastic comparisons of residual life time and inactivity time in series and parallel systems. These results are in addition to the existing results of Li & Zhang (2003) and Li & Lu (2003). We also present sufficient conditions for aging properties of the residual life time and inactivity life time of series and parallel systems. Some examples from Weibull and Gompertz distributions are provided to support the results as well.

On optimal operational sequence of components in a warm standby system

2018 ◽  
Vol 55 (4) ◽  
pp. 1014-1024 ◽  
Author(s):  
Maxim Finkelstein ◽  
Nil Kamal Hazra ◽  
Ji Hwan Cha
Keyword(s):  
Open Problem ◽  
Cumulative Exposure ◽  
Exposure Model ◽  
Virtual Age ◽  
Cumulative Exposure Model ◽  
Standby System ◽  
Stochastic Precedence ◽  
Warm Standby

Abstract We consider an open problem of obtaining the optimal operational sequence for the 1-out-of-n system with warm standby. Using the virtual age concept and the cumulative exposure model, we show that the components should be activated in accordance with the increasing sequence of their lifetimes. Lifetimes of the components and the system are compared with respect to the stochastic precedence order and its generalization. Only specific cases of this optimal problem were considered in the literature previously.

Petrolatum Prevents Irritation in a Human Cumulative Exposure Model in vivo

Dermatology ◽  
1997 ◽  
Vol 194 (3) ◽  
pp. 247-250 ◽  
Author(s):  
W. Wigger-Alberti ◽  
P. Elsner
Keyword(s):  
Cumulative Exposure ◽  
Exposure Model ◽  
Cumulative Exposure Model
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