Bayesian modelling of train door reliability

This article discusses the results of a study in Bayesian reliability analysis concerning train door failures in a European underground system over a period of nine years. It examines failure data from forty underground trains, which were delivered to an European transportation company between November 1989 and March 1991. All of the trains were put in service from 20 March 1990 to 20 July 1992. Failure monitoring ended on 31 December 1998. The goal of the study was to find models able to assess the failure history and to predict the number of failures in future time intervals in order to help the company determine the reliability level of the train doors before warranty expiration. The article describes the development and application of a novel bivariate Poisson process as a natural way to extend the usual Poisson models for analysing the occurrence of failures in repairable systems.

Probability Model for Data Redundancy Detection in Sensor Networks

Sensor networks are made of autonomous devices that are able to collect, store, process and share data with other devices. Large sensor networks are often redundant in the sense that the measurements of some nodes can be substituted by other nodes with a certain degree of confidence. This spatial correlation results in wastage of link bandwidth and energy. In this paper, a model for two associated Poisson processes, through which sensors are distributed in a plane, is derived. A probability condition is established for data redundancy among closely located sensor nodes. The model generates a spatial bivariate Poisson process whose parameters depend on the parameters of the two individual Poisson processes and on the distance between the associated points. The proposed model helps in building efficient algorithms for data dissemination in the sensor network. A numerical example is provided investigating the advantage of this model.

On a Voronoi aggregative process related to a bivariate Poisson process

We consider two independent homogeneous Poisson processes Π0 and Π1 in the plane with intensities λ0 and λ1, respectively. We study additive functionals of the set of Π0-particles within a typical Voronoi Π1-cell. We find the first and the second moments of these variables as well as upper and lower bounds on their distribution functions, implying an exponential asymptotic behavior of their tails. Explicit formulae are given for the number and the sum of distances from Π0-particles to the nucleus within a typical Voronoi Π1-cell.

On a Voronoi aggregative process related to a bivariate Poisson process

We consider two independent homogeneous Poisson processes Π0 and Π1 in the plane with intensities λ0 and λ1, respectively. We study additive functionals of the set of Π0-particles within a typical Voronoi Π1-cell. We find the first and the second moments of these variables as well as upper and lower bounds on their distribution functions, implying an exponential asymptotic behavior of their tails. Explicit formulae are given for the number and the sum of distances from Π0-particles to the nucleus within a typical Voronoi Π1-cell.

Some remarks on a counter process

In 1968 Lampard determined some limit distributions for a counter process in which the input and output are independent Poisson processes. In 1974 Phatarfod dealt with the generalizations of Lampard's formulas for the case when the input and output form a bivariate Poisson process; however, his reasoning is erroneous. The object of this paper is to determine the correct limit distributions for the generalized process.

Some remarks on a counter process

In 1968 Lampard determined some limit distributions for a counter process in which the input and output are independent Poisson processes. In 1974 Phatarfod dealt with the generalizations of Lampard's formulas for the case when the input and output form a bivariate Poisson process; however, his reasoning is erroneous. The object of this paper is to determine the correct limit distributions for the generalized process.