Promotional paper consists of: - Introduction, 5 chapters and a conclusion, complemented with 58 images, 9 charts, 7 attachments (annexes), resulting in 152 pages; a total of 47 information sources have been used. Keywords: Fatigue-crack; minimax-principle; Markov-chain; Semi-Markov-chains with reward; maintenance program. The promotional paper is about analysis of choice of maintenance frequency of constructions, subject to fatigue-crack development; research proposes original method to choose maintenance frequency. A computer program is developed to make use of required equations. Promotional paper incorporates synopsis of the development of the problem; different principles of the creation of maintenance frequency programs; applicable mathematical methods; proposed innovations and description of utilized mathematical methods; mathematical example and conclusion. Attachment holds print of the developed computer program script. A modern on renewal (restoration) theory based maintenance frequency planning program usually as a must takes into account only the service-life of the assembly. The offered method also takes into account the fatigue-crack growth trajectory. Existing methods consider the law of service-life layout to be a given value and a probability theory calculation is carried out. The developed methodology evaluates parameters of fatigue-crack growth based on examination results. According to the developed method, if the examination proves the set requirements of the prototype assembly are not met, the construction is not accepted into exploitation unless flaw is removed. This enables the use of MinMax approach. As a result the safety of the exploitation of the construction is ensured at any fatigue-crack growth parameter and layout peculiarity (since only constructions that met the set requirement are accepted into exploitation, while inadequate assemblies are not); The theory of the Semi-Markov chain processes with income parameters is used for the calculations. as a result, two major tasks are accomplished: - Task Nr 1: ensure safety; - Task Nr 2: manage exploitation expenses. Properly chosen frequency of the maintenances ensures the maximum amount of income while maintaining required safety.