scholarly journals Weak independence of events and the converse of the Borel–Cantelli Lemma

Author(s):  
Csaba Biró ◽  
Israel R. Curbelo
2000 ◽  
Vol 66 (2) ◽  
pp. 183-189 ◽  
Author(s):  
Donald E. Campbell ◽  
Jerry S. Kelly
Keyword(s):  

Author(s):  
Guilerme A. C. Caldeira ◽  
JoaquimAP Braga ◽  
António R. Andrade

Abstract The present paper provides a method to predict maintenance needs for the railway wheelsets by modeling the wear out affecting the wheelsets during its life cycle using survival analysis. Wear variations of wheel profiles are discretized and modelled through a censored survival approach, which is appropriate for modeling wheel profile degradation using real operation data from the condition monitoring systems that currently exist in railway companies. Several parametric distributions for the wear variations are modeled and the behavior of the selected ones is analyzed and compared with wear trajectories computed by a Monte Carlo simulation procedure. This procedure aims to test the independence of events by adding small fractions of wear to reach larger wear values. The results show that the independence of wear events is not true for all the established events, but it is confirmed for small wear values. Overall, the proposed framework is developed in such a way that the outputs can be used to support predictions in condition-based maintenance models and to optimize the maintenance of wheelsets.


1978 ◽  
Vol 85 (5) ◽  
pp. 363-364
Author(s):  
Frederick Stern
Keyword(s):  

2006 ◽  
Vol 152 (1) ◽  
pp. 143-155 ◽  
Author(s):  
François Maucourant

1980 ◽  
Vol 12 (02) ◽  
pp. 281-282
Author(s):  
F. Thomas Bruss
Keyword(s):  

1980 ◽  
Vol 17 (4) ◽  
pp. 1094-1101 ◽  
Author(s):  
F. Thomas Bruss

The general part of the Borel-Cantelli lemma says that for any sequence of events (An) defined on a probability space (Ω, Σ, P), the divergence of ΣnP(An) is necessary for P(An i.o.) to be one (see e.g. [1]). The sufficient direction is confined to the case where the An are independent. This paper provides a simple counterpart of this lemma in the sense that the independence condition is replaced by for some . We will see that this property of (An) may frequently be assumed without loss of generality. We also disclose a useful duality which allows straightforward conclusions without selecting independent sequences. A simple random walk example and a new result in the theory of ϕ -branching processes will show the tractability of the method.


2014 ◽  
Vol 614 ◽  
pp. 367-370 ◽  
Author(s):  
Chun Qin Zhang ◽  
Hui Zhang

Sugeno measure is a fuzzy measure. In this paper, we derive the Borel-Cantelli lemma for Sugeno measure. This result is a natural extension of the classical Borel-Cantelli lemma to the case where the measure tool is fuzzy. The properties of Sugeno measure are further discussed. Then the Borel-Cantelli lemma will be proven on Sugeno measure space. This work generalizes the research and applications of the Borel-Cantelli lemma.


1978 ◽  
Vol 6 (4) ◽  
pp. 699-700 ◽  
Author(s):  
Louis H. Y. Chen
Keyword(s):  

1966 ◽  
Vol 2 (4) ◽  
pp. 397-398 ◽  
Author(s):  
Guiseppe Gestri ◽  
Lamberto Maffei ◽  
Donatella Petracchi

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