Mathematical Model of Maintenance of Samples of Weapons and Military Equipment Using the Distribution of Time of Trouble-Free Operation of Products in the Form of Weibul's Law

Abstract

The article considers the mathematical model of maintenance of samples of armaments and military equipment according to the state with parameter control, for which the distribution of time of trouble-free operation of weapons in the form of Weibul's law is used as a model of failures. Probable physical distributions have a certain advantage over simply probable distributions, because their parameters can be determined on the basis of both statistical characteristics of failures and analysis of failures of the physical process. In addition, diffusion distribution laws, such as diffusion-monotone and diffusion-nonmonotonic distributions, are now the most relevant. These facts have significant practical value, which determines the relevance of the research. Also, the article considers the dependences of the coefficient of technical use of the object on different characteristics of the service system and the object itself are determined. For the mathematical description of the processes inherent in the maintenance system, the apparatus of semi-Markov random processes in the classical representation is used. Weibul's distribution law is one of the least used due to its complexity. The main results of the work are obtained by numerical method. The dependences obtained as a result of the calculations show the existence of the optimal period of preventive maintenance of the object of control, in which the maximum value of its coefficient of technical use is achieved. The result of the work allows to establish the quantitative dependence of the coefficient of technical use on the reliability of control means, scale and form in the form of Weibul's distribution law in a wide range of periodicity of preventive maintenance.