Development of Stochastic Models for Occupational Hazards Risk Assessment

Abstract

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.

Improvement of risk management principles in occupational health and safety

“…Instead, the known methods of mathematical modeling of random processes are given in IEC/ISO 31010:2019 in a lim ited form and are not in the list of the recommended ones for complex risk evaluation not only by criterion SA but even A [14]. However, just on the basis of these methods it is possible to develop methodological support for the complex imple mentation of the evaluation stage, which will take into account all the objective features (random, dynamic characteristics, and so on) of negative NF impact on the employee, within the "manmachineenvironment" system [20]. In addition, the use of appropriate mathematical tools allows developing a PC software, which greatly simplifies the use of methodological support in organizations.…”

“…However, in contrast to the one pro posed below, the existing method provides using Markov chains for the risks evaluation, which allows considering tasks only under the conditions of the given amount of states and continuous time [14]. Such conditions do not comply with real (dynamic and random in time) characteristics of the impact of NF on the employee, therefore the results of risk evaluation cannot be as objective [20].…”

“…In this case, the severity of the consequences of the injury is determined by the recovery time (treatment) of the employee. The risk evaluation stage involves a preliminary solution of the differential equations system (analytically or with the help of the Matlab software package) and the definition of the follow ing indicators [20]: the probability that the accumulation level of the HPF impact on the employee exceeds normalized values 00 01 0 0…”

“…This comparison takes place within the Risk evalua tion substage and accordingly provides for the implementa tion of the following condition r 0 ≤ r. (9) This expression can be considered correct, because in the development of methodological support, both for the stage of determining of resources and for the stage of risk assessment (2-8) the condition (1) was taken into account. Therefore, given that the controlled parameters for models (6)(7)(8) are the intensity of the NF impact on the employee, the task of the risk assessment stage is the need to set such values of con trolled parameters that will ensure (according to the definition r 0 ) condition (9) [20]. The result of condition (9) indicates that the planning procedure can be considered successfully com pleted.…”

“…recommended Books. An analytical way to solve the dif ferential equations system to obtain the required probabilities (6-8) is given in [20].…”