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Concept of Modeling and Optimization of Reliability of Complex System by Minimum Risk Criterion

The paper discusses the approach to modeling the reliability of a complex system, based on the description of reliability by a continuous function of the “natural” aging of its components by a differential equation with a centered random component. In general, the model is a system of differential equations, where the blocks are taken into account with discrete failure (running/ not running) and deviations from the center of a given allowable range of key characteristics in the right parts for each function. Wherein, the loss function can be defined as a quadratic function within the tolerance, and with a zero value inside the tolerance interval and a linear increase outside this interval (in accordance with “tolerance thinking”). The probability of occurrence of functional unit failure was chosen as the main variable; it is used to assess the risk in addition to indirectly evaluating the reliability of the system along with the severity of the consequences of failure. The model provides for taking into account the probability of the accidental repeated occurrence of dangerous event at a constant intensity of flow of the failures of replaced blocks. The characteristics of the blocks are used for assessing the risk of the current state and replacing failed ones blocks (the number of block repairs, the level of qualification of the repair personnel, the worked time before repair, the spending time in the reserve and some other characteristics, which determine the planned life of the block). These parameters are involved in the formation of some model coefficients. The model can be used both in simulation of the process of system functioning, and in conjunction with its functioning in real time.