The topic of the study is to consider the possibility of using experimental planning methods to mathematically describe areas of performance in relation to marine electromechanical systems. A definition is given and a graphic illustration of the field of operability is provided. It is shown that information about the boundary of the field of operability allows solving the most important tasks of controlling the state of ship electromechanical systems of various functional purposes. Possible ways of solving the problem of constructing a field of efficiency and the difficulties of their practical implementation are given. The method of analytical description of the operability domain is considered, which assumes an independent approximation of each hypersurface that makes up the operability domain. It is shown that for such an approximation it is convenient to use polynomial dependencies, which can be obtained as a result of using experimental planning methods. The main advantages of this approach are considered, including the possibility of solving the problem in the case of a high dimension of the space of primary parameters, in the space of which the area of operability is built. It is noted that in order to obtain a unified analytical description of the field of operability, the properties of logical R-functions can be used, which make it possible to make the transition from logical functions to analytical dependencies. It is proved that polynomial dependencies have the properties of R-functions and can be used in such a transformation. The resulting analytical description of the health area is universal and does not depend on the configuration of the area itself. Unlike the known methods of analytical approximation of the field of operability, it is characterized by an exceptionally low methodological error and allows us to solve with high reliability the problem of parametric synthesis of marine electromechanical systems according to the criterion of the reserve of operability, as well as the tasks of evaluating and predicting their condition during operation. The considered example clearly demonstrated the sequence of solving the problem of analytical description of the field of operability and allowed us to conclude about the complex configuration of this area even for special cases and the simplest electromechanical systems.
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