Search results for "Counting process"

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Reliability analysis of processes with moving cracked material

2015

Abstract The reliability of processes with moving elastic and isotropic material containing initial cracks is considered in terms of fracture. The material is modelled as a moving plate which is simply supported from two of its sides and subjected to homogeneous tension acting in the travelling direction. For tension, two models are studied: (i) tension is constant with respect to time, and (ii) tension varies temporally according to an Ornstein–Uhlenbeck process. Cracks of random length are assumed to occur in the material according to a stochastic counting process. For a general counting process, a representation of the nonfracture probability of the system is obtained that exploits condi…

FOS: Computer and information sciencesStochastic modellingBoundary (topology)02 engineering and technologyComputational Engineering Finance and Science (cs.CE)0203 mechanical engineeringfirst passage timeComputer Science - Computational Engineering Finance and Sciencestochastic modelMathematics040101 forestryta214Counting processTension (physics)Applied Mathematicsta111Mathematical analysisIsotropyOrnstein–Uhlenbeck process04 agricultural and veterinary sciencesmoving material020303 mechanical engineering & transportsfractureModeling and Simulation0401 agriculture forestry and fisheriesOrnstein-Uhlenbeck processFirst-hitting-time modelConstant (mathematics)Applied Mathematical Modelling
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A Random Field Approach to Transect Counts of Wildlife Populations

1991

Line transect counting of a wildlife population is considered a sampling from a planar marked point process, where the marks describe the detectability of the animals. Sampling properties of transect counts and a new density estimator are derived from a counting process, which is a shot-noise field induced by the marked point process. A general formula for the sampling variance of a transect is derived and applied to compare five common types of transects. Some stereological connections of transect sampling and density estimators are shown.

Statistics and Probabilityeducation.field_of_studyRandom fieldCounting processCovariance functionPopulationSampling (statistics)EstimatorGeneral MedicineDensity estimationStatisticsStatistics Probability and UncertaintyeducationTransectMathematicsBiometrical Journal
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