The general model of a complex system changing its safety structure, its components safety parameters and its operation cost during the variable operation process and linear programming are applied to optimize the system operation process in order to get the system operation cost optimal values. The optimization problem allowing to find the optimal values of the transient probabilities of the complex system operation process at the particular operation states that minimize the system unconditional operation cost mean value in the safety states subset not worse than a critical system safety state under the assumption that the system conditional operation cost mean values in this safety state subset at the particular operation states are fixed is presented. Further, the procedure of finding the optimal values operation cost is presented and applied to the exemplary complex technical system.
Modelling and prediction of the operation and reliability of technical multistate ageing systems related to their operation processes called complex systems are briefly presented and applied to prediction of the operation processes and reliability characteristics of an exemplary complex non-homogeneous system composed of a series-parallel and a series-“m out of l” subsystems linked in series, changing its reliability structure and its components reliability parameters at variable operation conditions. Further, the linear programming is proposed to the operation and reliability optimization of complex technical systems operating at variable operation conditions. The method consists in determining the optimal values of limit transient probabilities at the system operation states that maximize the system lifetimes in the reliability state subsets. The proposed method is practically applied to the operation and reliability optimization of the considered exemplary complex system.
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