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It is well known that the sidelobe structure of a reflector antenna is highly susceptible to random surface errors, and that in most applications it is not adequate to investigate only the average behavior of the antenna. In this study, an attempt is made to determine the probability distribution of the sidelobe level of a reflector antenna subject to some random surface errors. Specifically, the random pattern function is considered and its sidelobe level studied using the level-upcrossing theory. Both the degradation of the maximum sidelobe and the degradation of the sidelobe region with respect to an International Radio Consultative Committee (CCIR) sidelobe envelope are obtained. The theoretical results are found in excellent agreement with those obtained by Monte Carlo simulations. Finally, some useful tolerance charts are presented.