As one of the directions of hazardous production facilities reconstruction, it is possible to outline the implementation of the activities aimed at maintaining and (or) increasing the sustainability and safety of their operation. However, it should be noted that conducting these activities involves costs of certain resources, which are often limited.

The objective of the article is to present the approach to substantiation of the selection of the activities on improving the sustainability and safety of hazardous production facilities considering limited resources.

To achieve this goal, an approach based on the gradient method of solving extremal problems is proposed. In this case, the probability of the stable and safe operation of the object is considered as a target function. The considered function interconnects the probability of trouble-free operation of the object itself, the reliability of the results of the subsystem analysis of the object technical condition, the distribution function of the work execution time on restoration of the object operational state, the joint distribution function of the protection subsystem response time, and the duration of the technical condition analysis.

The criterion for selecting the priority of the conducted activities is the relative values of the gradient increments, which make it possible in the best way to select the factor, based on which the works should be carried out related to improvement of the target function values. Subsequent iterations are associated with the assessment of costs required for completion of the next priority activity. They are completed at the moment the resources are free from limits. 

The implementation of the proposed approach allows to reasonably select the direction of work on the modernization of technical systems, as well as to obtain the quantitative assessment of its results.