The paper presents a problem statement of guaranteed control of production output by use of a probabilistic criterion that requires presence of the product output within specified limits with a given probability. Within the problem statement, the existence of the controls is considered in the form of sufficient mutual conditions which the initial problem characteristics are to meet to. Deriving the conditions is based on applying corresponding probabilistic inequalities enabling one to establish a connection between the limits for the production output, the amount of the mean square deviation of the production output, and the required probability of presence of the production output within the specified limits. The probabilistic conditions obtained are also shown to be applicable within a distribution free input/output system identification problem statement with a probabilistic criterion. The paper has been supported by a grant of the Russian Foundation for Basic Researches (RFBR): project 12-08-01205-a.