ABSTRACT: The model of system safety impacted by operation process is created and the procedure of its safety in the safety state subsets not worse than the critical safety state maximization is proposed. The model of system operation total costs in the safety state subsets is introduced and the procedure of its operation total cost in the safety state subset not worse than the critical safety state minimization is presented. To analyze jointly the system safety and its operation cost optimization, we propose determining the optimal values of limit transient probabilities of the system operation process at the particular operation states that allows to find the best system safety function and other safety indicators, utilizing the created system safety model and linear programming. Next, to find the system operation total costs in the safety state subsets, corresponding to this system best safety indicators, we replace the limit transient probabilities at the particular operation states, existing in the formula for the system operation total costs in the safety state subsets, by their optimal values existing in the formulae for the coordinates of the system safety function after maximization. On the other hand, to analyze jointly the system operation cost and it’s safety optimization, we propose the procedure of determining the optimal values of limit transient probabilities of the system operation process at the particular operation states that allows to find minimal system operation total cost in the safety state subset not worse than the critical safety state, using the created system operation cost model and linear programming. After that, to find the system conditional safety indicators, corresponding to this system minimal total operation cost in the safety state subset not worse than the critical safety state, we replace the limit transient probabilities at particular operation states, existing in the formula for the system safety function coordinates, and for remaining system conditional safety indicators by their optimal values existing in the formulae for the system minimal total cost in the safety state subsets not worse than the critical safety state. The created models are applied separately and jointly to the maritime transportation system. Moreover, to fulfil the obtained maritime transportation system optimal safety and operation cost results the modifications of its operation process is proposed. The evaluation of results is performed and future research in the field of the complex systems, including maritime transportation systems, safety and their operation costs joint analysis and optimization is proposed.

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