The aim of this paper is to present theoretical starting points in the field of risk analysis. This paper is formulated as a systematic overview of the latest knowledge and trends, which are supported by the simulation of selected risk parameters intended for the prediction of adverse events. The analysis and assessment of technical risk allow not only for indicating negative events detected in a process but also for taking corrective measures based on systematic reductions in technical system failures. This article refers to the use of mathematical experiments of risk modelling and simulation because mathematical modelling and simulation are very suitable methods for the analysis, modelling, and prediction of random phenomena in risk theory and assessment. The analytical approach is based on stochastic and deterministic risk modelling procedures and on the principle of risk evaluation through the effects of two factors: the probability of occurrence of negative events and consequences and their impact from the point of view of malfunctions. The analytical approach is based on a mathematical model that considers the intersection of two phenomena in terms of expressing the probability of two different statistical distributions in a stochastic expression. The analysis and assessment of technical risk allow not only for indicating negative events detected in a process but also for taking corrective measures. The aim of this article is to formulate a method that can be used to set and evaluate the technical risk of the cutting process from an organizational point of view.
