The article discusses the mathematical model of technical condition-based maintenance of weapon systems. The model his developed based on a semi-Markov stochastic process. The diffusion-monotonic (DM) distribution law, which is specific for airfield technical condition-based maintenance of aircraft, is has been used as a failure model, and type I errors are considered. For standard operating conditions, graphs of the dependence of the coefficient of technical use and specific costs per hour of operation in good condition from the basic parameters are shown. The optimal maintenances interval ensuring maximum maintenance coefficient value has been proved. The principal results have been achieved by using multiple calculation method.

The article is of interest to health professionals operating in the system of the Ministry of defense of Ukraine and Armed Forces of Ukraine and other state authorities, institutions and non-government organizations. Also, the results of the study will be useful to the representatives of the medical service, as service is a direct participant in the process of evaluating the effectiveness of the military personnel’s medical examination system. The place and role of the clinical examination of personnel in the health care system have been established. This has allowed to identify the internal and external factors in the context of the issues of this article. Internal and external factors were investigated in the context of managed and unmanaged factors. The paper presents a mathematical model of the medical care for servicemen who undergo medical examinations with using a semi-Markov random process. A quantitative criterion for the effectiveness of health care, called the employability ratio, is proposed. To establish the dependence of the employability ratio on the model parameters, an exponential law of time distribution between diseases was used.  Such a law can be considered as a characteristic of the military personnel of a relatively young age. The results of this study are the starting point for solving the scientific task of substantiating the scientific and methodological apparatus for assessing the effectiveness of the prophylactic medical examination in the system of medical support of servicemen of the Ministry of defense of Ukraine and Armed Forces of Ukraine. In further studies will be shown the dependence of the employability ratio on the model parameters, as well as the cost of staying a serviceman in a healthy condition.

The emergence of reliability as an applied mathematical discipline is associated with the 50-60 years of the last century, when large and complex technical systems began to be created in various branches of technology. In this regard, an acute reliability problem arose, that is, ensuring the functioning and operability of these complex and expensive systems. The whole variety of reliability studies is aimed at solving the following three problems: assessment and prediction of product reliability at the design stages (a priori methods); experimental evaluation of reliability indicators, that is, confirmation of the projected level of reliability according to the results of tests or operation (posterior methods); taking measures to achieve and ensure a given level of reliability by optimizing the maintenance strategy, redundancy, spare parts, etc. (optimization problems) The traditional has developed a certain division in the areas of theory and practice of reliability of machines (mechanical objects, technical systems containing mechanical components) and equipment (electronic products, technical devices containing electronic and radio elements). The main tasks of reliability of machines and equipment - the establishment of patterns of failure and the assessment of quantitative indicators of reliability - can be solved in two different ways. To date, the direction based on the use of only probabilistic concepts (purely probabilistic theory) has received the greatest development in the theory and practice of reliability. The second way to establish quantitative indicators of reliability, in contrast to a purely probabilistic approach, is based on the study of mechano-physico-chemical properties and some physical parameters of products characterizing the technical condition of the latter using probabilistic methods. The methodology for establishing quantitative reliability indicators based on the study of certain physical parameters characterizing the technical condition of products consists in identifying the kinetic laws of degradation processes (building mathematical models of degradation processes) and determining the analytical relationship between these laws and reliability indicators. The article discusses the use of diffusion-nonmonotonic distribution for modeling the process of operation of electronic equipment. Particular attention is paid to the determination of point estimates of distribution parameters based on the results of operational observations.