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This paper deals with some fundamental guidelines for the establishment of a stochastic arc model. Its aim is to describe the well known statistical behavior of the interrupting limit of circuit breakers taking into account short time fluctuations of the arc properties. This stochastic arc model is based on a phenomenological arc description regarding the switching arc as an electric two-pole. The arc parameters are no longer understood as deterministic functions but as stochastic processes. Their probability density distributions and the respective autocovariance and crosscovariance functions are the mathematical means to establish the model. Pseudorandom generators are used to compute switching processes of an electrical network connected to a stochastic arc. Experiments of an SF6 model circuit breaker were carried out with respect to the statistical behavior of its current, arc voltage, conductivity, and interrupting limit. From these experiments the necessary arc parameters were taken in an iterative strategy. With these parameters it was possible to reach good agreement between measured and calculated values of the failure probability of the breaker under test.