Purpose. Substantiation of the urgency of the scientific principles elaboration on evaluating risks of occupational danger occurrence for use in the occupational health and safety management systems (OHSMs). Methodology. The research on risk evaluation of occupational danger occurrence problem has been conducted by means of study with subsequent theoretical analysis of:-the normative legal documents of Ukraine concerning risk management in the occupational safety field;-risks evaluation purposes;-methodology of risk identification;-procedures and steps of evaluating risks of occupational danger occurrence. findings. The legal documents concerning both the risk evaluation and management regarding occupational danger occurrence were analyzed. On the basis of the analysis, the problems concerning the purposes, terminology and methodology of risk evaluation processes were revealed. The analysis of the main stages of general risk evaluation was conducted and system problems were identified which significantly influence the evaluation implementation quality and objectivity and concurrently cast doubt upon feasibility of evaluation procedures within existing standards. The urgency of the scientific principles elaboration on evaluating the risks of occupational danger occurrence was substantiated, which will essentially contribute to the evaluation procedure simplification as well as to improvement of its quality and objectivity of implementation. Originality. For the first time, the urgency of the issue was substantiated; both principles and directions for the scientific principles elaboration on evaluation of risks of occupational danger occurrence are formulated for use in the occupational safety management systems in Ukraine and internationally. Practical value. The obtained results will be used as an analytic basis contributing to elaboration of scientific principles of risk evaluation regarding occupational danger occurrence.

Introduction.  For today there are about a hundred high-quality, quantitative and combined risks evaluation techniques, but none of them is suitable for use in the field of occupational healthy and safety since it does not take into account the dynamic nature of the random hybrid influence on the employee of dangerous and  harmful productive factors within "man-machine-environment" systems.  For a description of the actual process of hybrid influence of dangers on a employee, it is necessary to use a special subclass of Markov processes with drift, the use of which for risk evaluation in the field of occupational healthy and safety is still unknown.                 Purpose.  Development of methodological bases for application of Markov processes with drift to evaluate the risks of occupational dangers origin.                 Methods.  A special method of quantitative analysis of complex systems - Markov analysis was used to simulate the random processes of negative influence of dangers on the employee.                 Results.  A special subclass of Markov processes with drift for the possibility of simulation the hybrid nature of the influence on the employee of dangerous and  harmful productive factors was first substantiated and proposed for the risks evaluation procedure in "man-machine-environment" systems.  A system of differential equations and limit conditions for finding the limit distribution of the random process probabilities of occupational dangers origin in "man - machine - environment" systems was obtained.                 Conclusions.  The limit distribution of the random process probabilities of occupational dangers origin in "man - machine - environment" systems was determined limiting and expressions for the determination of a number of key indicators that can be used to evaluate the risks level of occupational dangers origin were obtained.  It is advisable to develop the further research in the direction of the possibilities of realization of the proposed modeling scheme within combination of analytical approach and simulation modeling.

IMproveMent of rIsK MAnAGeMent prIncIples In occupAtIonAl heAlth AnD sAfety purpose. To improve the risk management principles in occupational health and safety. Methodology. In study the following set of scientific methods was used: analysis of scientific and technical literature and inter national normative legal documents on the construction and operation of occupational health and safety management systems; probabilisticstatistical methods; the theory of Markov processes; methods of formalization. findings. The main problems that make it impossible to objectively implement the PDCA process in modern occupational health and safety management systems in organizations are identified. It is noted that the identified problems are related to: uncer tainty of the requirements of ISO 45001:2018 regarding the purposes, sequence and results of each procedure of the PDCA process in occupational health and safety; inadequacy of methodological support of the main stages of the Plan procedure; lack of practi cal opportunities for objective implementation of Do, Check, Act procedures. The prerequisites are established for the transition of the systems of health care (HC) and occupational safety support (OSS) to the new concept of proactive risk management (based on the operation of two small cycles within the PDCA process), which allows ensuring the existence of objective relationships be tween all procedures of the PDCA process; increasing the efficiency of the HC and OSS systems through providing the ability to manage the impact of negative factors on the employee by certain parameters; determination of clear cause and effect relationships between the parameters of the impact of negative factors on the employee and the incident, as well as other benefits. The possibil ity of application of the automated system of complex protection of employees from occupational dangers was substantiated to solve practical problems of the new concept of PDCA in the HC and OSS systems in the organizations. originality. For the first time, the concept of proactive risk management based on the principles of small cycles in the PDCA process was substantiated and proposed for use in the HC and OSS systems. practical value. The obtained results will be used for development of projects of changes in the maintenance and structure of

Purpose: Elaborate stochastic models to comprehensive evaluation of occupational risks in “man - machine - environment” systems taking into account the random and dynamic nature of the impact on the employee of negative factors over time. Design/methodology/approach: Within study, the methods of probability theory and the theory of Markov processes - to find the limit distribution of the random process of dynamic impact on the employee of negative factors over time and obtain main rates against which the level of occupational risks within the "man - machine - environment" systems can be comprehensively evaluated; Erlang phases method, Laplace transform, difference equations theory, method of mathematical induction - to elaborate a method of analytical solution of the appropriate limit task for a system of differential equations in partial derivatives and appropriate limit conditions were used. Findings: A system of differential equations in partial derivatives and relevant limit conditions is derived, which allowed to identify the following main rates for comprehensive evaluation of occupational risks in systems "man - machine - environment": probability of excess the limit of the employee's accumulation of negative impact of the harmful production factor; probability of the employee’s injury of varying severity in a random time. An method to the solution the limit task for a system of differential equations, which allows to provide a lower bounds of the probability of a certain occupational danger occurrence was elaborated. Research limitations/implications: The elaborated approach to injury risk evaluation is designed to predict cases of non-severe injuries. At the same time, this approach allows to consider more severe cases too, but in this case the task will be more difficult. Practical implications: The use of the elaborated models allows to apply a systematic approach to the evaluation of occupational risks in enterprises and to increase the objectivity of the evaluation results by taking into account the real characteristics of the impact of negative factors on the employee over time. Originality/value: For the first time, a special subclass of Markov processes - Markov drift processes was proposed and substantiated for use to comprehensive evaluation of occupational risks in “man - machine - environment” systems.

Introduction. The main disadvantage of existing methods and models of risk assessment in the field of occupational safety is the failure to take into account the dynamic characteristics of the processes of random hybrid impact on the em-ployee of hazardous and harmful production factors. Such negative impact characteristics are observed during the opera-tion of any real "man-machine-environment" system, therefore, it is imperative to take into account the risk assessment.Purpose. Development of stochastic models for assessing the risks of occupational hazards in the systems of "man-machine-environment".Methods In the development of stochastic models for assessing the risks of occupational hazards, the theory of Markov processes was used, while the boundary problem was solved - the method of the Erlang fictitious phases. Results. To find the limiting probability distribution of the random process of occupational dangers origin in sys-tems "man-machine-environment", a system of differential equations in partial derivatives and corresponding limiting78 Вісник ЛДУБЖД, №19, 2019 conditions was derived, which made it possible to determine the following basic indicators for risks evaluation of oc-cupational dangers origin:– the probability of exceeding the normalized (hygiene standards) accumulation of negative influence of the harm-ful production factor;– the probability that the effects of the negative influence on the employee of the harmful factor will be completely absent at a random period;– the probability of employment injury by an employee at a random period;– the average level of accumulation in employee of negative influence against the harmful production factor, etc.It is emphasized that such indicators can be used as criteria, provided that approach of risks evaluation will be im-plemented at the state level. A method of solving the limited problem for a system of differential equations based on Laplace transformation for the case of the Erlang distribution of working and non-working periods is proposed. Conclusions. Stochastic models for risk assessment in "human-machine-environment" systems are developed, which allow to estimate the level of risk of occupational hazards according to the basic indicators characterizing the level of occupational safety. A method of solving the boundary value problem for a system of differential equations based on Laplace transformation for the case of the Erlang distribution of working and non-working time periods is developed. The obtained solution allows to find the moments of probabilistic distribution of the level of accumulation of negative influence from the action of harmful production factors in the body of the worker. hat gives the possibility of using Chebyshev's inequality to give a lower estimate of the probability of exceeding the level of the indicated nega-tive influence of the maximum - admissible (normalized) values. In the future, the practical interest is the consideration of a random process for cases of serious injury, when the employee needs a long time to undergo treatment and rehabili-tation from the consequences of injuries received during the failure of production equipment of the second type. This problem is solved within the framework of the proposed approach and presented in the study.