Title :
A kinetic model of failure occurrences in a chain reaction and an analysis using Bernstein polynomials and the Brownian motion with some relativity
Author :
Wagatsuma, Hiroaki
Author_Institution :
Dept. of Brain Sci. & Eng., Kyushu Inst. of Technol., Kitakyushu, Japan
Abstract :
Failure occurrences in a system have been analyzed by using a stochastic process model such as Markov process. The event probability of the rare accident is conventionally described as a multiplication of probabilities of failure occurrences of individual components in the system, which is derived from the strong assumption of an independent probabilistic distribution. In this paper, I focus on a process of occurrence of lethal accidents with causal influences and cooperative actions and propose a kinetic model of failure occurrences in a chain reaction for mathematical analyses. In this theory, the cooperative Brownian motions are simulated as a model of the rare event if it passes through a narrow hole in walls that described by Bernstein polynomials.
Keywords :
Brownian motion; accidents; failure analysis; polynomials; reliability theory; risk analysis; statistical distributions; stochastic processes; Bernstein polynomial; chain reaction; cooperative Brownian motion; cooperative action; event probability; failure occurrence; independent probabilistic distribution; kinetic model; lethal accident occurrence process; mathematical analyses; rare accident; relativity; stochastic process model; Bézier curve; Ergodic theory; binomial theorem; de Casteljau´s algorithm; recursive protocol;
Conference_Titel :
Soft Computing and Intelligent Systems (SCIS) and 13th International Symposium on Advanced Intelligent Systems (ISIS), 2012 Joint 6th International Conference on
Conference_Location :
Kobe
Print_ISBN :
978-1-4673-2742-8
DOI :
10.1109/SCIS-ISIS.2012.6505276
