A kinetic model of failure occurrences in a chain reaction and an analysis using Bernstein polynomials and the Brownian motion with some relativity

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.