## 1 Introduction  
In complex human-machine systems, reliability is a key parameter. The human factor often plays a crucial role, particularly in probabilistic safety assessments of the system. Human errors are often the cause of negative events, and the contribution of human activity to system reliability and safety is often significant. In his work, [PERSON] [1] defines human reliability as the ability of an individual to perform tasks without failure over a certain period of time or number of attempts. This reliability depends on various factors, such as the individual's capabilities, working environment conditions, and the design of the systems with which the person interacts. Human reliability is not easy to determine or predict. This is because it is not an isolated act or a single decision but a combination of various influences, causes, and factors. Over the years, several approaches to human reliability analysis (HRA) have developed. This progress has led researchers to examine information more closely to determine the most appropriate approach for HRA. These methodologies can be divided into three main categories: first-, second-, and third-generation methods [2]. First-generation methods: These methods are based on static models and primarily use simple techniques to assess the probability of human errors. They are oriented on the assumption that errors can be quantified using fixed factors such as human capabilities and the environment. These techniques are often used to analyze repetitive operations in stable conditions but tend to ignore the dynamic aspects of complex systems. Second-generation methods: These methods are more sophisticated and take into account the system's dynamics, as well as the interaction between humans, machines, and the environment. They consider various factors that may affect human performance, such as stress, fatigue, and other psychological or physiological factors. Second-generation methods focus more on analyzing task complexity and the impact of human behavior in real operational conditions. Third-generation methods: These methods are the most advanced and include sophisticated quantitative models that allow for more detailed and flexible assessment of human reliability. These methodologies often use simulation-based models and involve various tools that allow for modeling interactions between humans, machines, and systems. The third generation emphasizes complex, dynamic, and unpredictable factors that may affect human performance in critical situations. The authors in this paper critically evaluate each of these generations and emphasize that although the methods have evolved, there are still certain limitations in effectively modeling human reliability in real, complex, and dynamic systems. Despite these reservations, these methods remain useful and many are commonly used for quantitative risk assessment [3]. Second-generation methods, a term introduced by [PERSON] [4], aim to address the shortcomings of traditional approaches, specifically the following:  
* Offering guidance on potential and likely decision-making pathways for operators, based on mental process models from cognitive psychology;
* Expanding the understanding of errors beyond the typical binary classification (omission-commission), acknowledging the significance of \"cognitive errors\";
* Considering the dynamic nature of human-machine interaction, which can serve as a foundation for developing simulators to assess operator performance. The problem lies in the fact that we often need to design systems with extremely high reliability, often requiring an overall failure rate of less than 1 in 10 million (i.e., 1 in 10\({}^{7}\)). Designing and analyzing such systems requires a deep understanding of human behavior under all possible circumstances that may occur during their operation and management. In recent years, the limitations and shortcomings of second-generation methods have led to the development of new third-generation methodologies [5].