Stochastic properties of two general versions of the residual lifetime at random times

2018 ◽  
Vol 34 (4) ◽  
pp. 528-543 ◽  
Author(s):  
Xiaohu Li ◽  
Rui Fang
Keyword(s):  
Residual Lifetime ◽  
Stochastic Properties ◽  
Random Times

scholarly journals On the Residual and Inactivity Times of the Components of Used Coherent Systems

2012 ◽  
Vol 49 (2) ◽  
pp. 385-404 ◽  
Author(s):  
S. Goliforushani ◽  
M. Asadi ◽  
N. Balakrishnan
Keyword(s):  
Dependent Measure ◽  
Time Dependent ◽  
Residual Lifetime ◽  
Coherent System ◽  
Reliability Engineering ◽  
Coherent Systems ◽  
Distributed Components ◽  
Technical Systems ◽  
Stochastic Properties ◽  
Independent And Identically Distributed

In the study of the reliability of technical systems in reliability engineering, coherent systems play a key role. In this paper we consider a coherent system consisting of n components with independent and identically distributed components and propose two time-dependent criteria. The first criterion is a measure of the residual lifetime of live components of a coherent system having some of the components alive when the system fails at time t. The second criterion is a time-dependent measure which enables us to investigate the inactivity times of the failed components of a coherent system still functioning though some of its components have failed. Several ageing and stochastic properties of the proposed measures are then established.

scholarly journals On the Residual and Inactivity Times of the Components of Used Coherent Systems

2012 ◽  
Vol 49 (02) ◽  
pp. 385-404 ◽  
Author(s):  
S. Goliforushani ◽  
M. Asadi ◽  
N. Balakrishnan
Keyword(s):  
Dependent Measure ◽  
Time Dependent ◽  
Residual Lifetime ◽  
Coherent System ◽  
Reliability Engineering ◽  
Coherent Systems ◽  
Distributed Components ◽  
Technical Systems ◽  
Stochastic Properties ◽  
Independent And Identically Distributed

In the study of the reliability of technical systems in reliability engineering, coherent systems play a key role. In this paper we consider a coherent system consisting of n components with independent and identically distributed components and propose two time-dependent criteria. The first criterion is a measure of the residual lifetime of live components of a coherent system having some of the components alive when the system fails at time t. The second criterion is a time-dependent measure which enables us to investigate the inactivity times of the failed components of a coherent system still functioning though some of its components have failed. Several ageing and stochastic properties of the proposed measures are then established.

scholarly journals Network Reliability Modeling Based on a Geometric Counting Process

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 197 ◽  
Author(s):  
Somayeh Zarezadeh ◽  
Somayeh Ashrafi ◽  
Majid Asadi
Keyword(s):  
Network Lifetime ◽  
Counting Process ◽  
Network Reliability ◽  
Stochastic Order ◽  
Reliability Function ◽  
Residual Lifetime ◽  
Reliability Modeling ◽  
Arrival Times ◽  
Network States ◽  
Stochastic Properties

In this paper, we investigate the reliability and stochastic properties of an n-component network under the assumption that the components of the network fail according to a counting process called a geometric counting process (GCP). The paper has two parts. In the first part, we consider a two-state network (with states up and down) and we assume that its components are subjected to failure based on a GCP. Some mixture representations for the network reliability are obtained in terms of signature of the network and the reliability function of the arrival times of the GCP. Several aging and stochastic properties of the network are investigated. The reliabilities of two different networks subjected to the same or different GCPs are compared based on the stochastic order between their signature vectors. The residual lifetime of the network is also assessed where the components fail based on a GCP. The second part of the paper is concerned with three-state networks. We consider a network made up of n components which starts operating at time t = 0 . It is assumed that, at any time t > 0 , the network can be in one of three states up, partial performance or down. The components of the network are subjected to failure on the basis of a GCP, which leads to change of network states. Under these scenarios, we obtain several stochastic and dependency characteristics of the network lifetime. Some illustrative examples and plots are also provided throughout the article.

Some Further Evidence on the Stochastic Properties of Systematic Risk

1987 ◽  
Vol 60 (3) ◽  
pp. 425 ◽  
Author(s):  
Daniel W. Collins ◽  
Johannes Ledolter ◽  
Judy Rayburn
Keyword(s):  
Systematic Risk ◽  
Stochastic Properties

Ehrenfest urn models

1965 ◽  
Vol 2 (02) ◽  
pp. 352-376 ◽  
Author(s):  
Samuel Karlin ◽  
James McGregor
Keyword(s):  
Exponential Distribution ◽  
Continuous Time ◽  
Random Variables ◽  
Independent Random Variables ◽  
Urn Models ◽  
Time Intervals ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Random Times

In the Ehrenfest model with continuous time one considers two urns and N balls distributed in the urns. The system is said to be in stateiif there areiballs in urn I, N −iballs in urn II. Events occur at random times and the time intervals T between successive events are independent random variables all with the same negative exponential distributionWhen an event occurs a ball is chosen at random (each of theNballs has probability 1/Nto be chosen), removed from its urn, and then placed in urn I with probabilityp, in urn II with probabilityq= 1 −p, (0 <p< 1).

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