Model of preventive replacements of complex systems elements depending on the operation time and the number of failures

Abstract

Modern conditions of economic activity of civil aviation operators make actual the problem of economically feasible measures for the organization of technical operation and maintenance of industry equipment, in particular, means of radio technical support for flights and aeronautical telecommunications. At the same time, it is obvious that these means need to be transferred to maintenance on a condition, which, in turn, causes the need to solve the problems related to determining the time for the preventive replacement of elements which diagnosable parameters can reach limit values. This paper presents an algorithm for estimating the optimal replacement of elements using the conditional probabilistic characteristic method for systems with a long period of operation and having a fixed number of failures. An assessment of the accuracy of determining the desired parameter is carried out, provided that its changes have deterministic and random components. The mathematical expectation and variance of the obtained estimate are found. Provided that the time of means operation between restorations (repairs) tends to decrease with an increase in the number of failures, the average number of final failures is obtained that satisfies the Volterra integral equation. To analyze the cost of restoration within the framework of the proposed model, an expression was found for the unit cost of work, depending on the accepted replacement rule and the duration of the expected cycles. Taking into account the mathematical expectation of the latter and associated costs, a two-dimensional optimal replacement rule is formed, and the expediency of using such a replacement period that minimizes the maximum average costs is shown. The obtained results are useful in organizing activities for preventive maintenance of radio technical support for flights and aeronautical telecommunications at various stages of their life cycle.