## 1 Introduction
The key aspect of failure removal time is the quick identification and localization of threats to avoid the risk of cascading failures [42]. Failure time can be defined as the time elapsed from the moment an incorrect operation of the system was detected until the irregularity is removed and the power supply is restored [43]. The articles presented in this literature review can be divided into several basic groups. The first group will consist of publications in which the authors present their formulas for determining the reliability of power line or transformer operations. Examples of such studies are [44; 45; 46]. [PERSON] and his team [45] focused on analyzing the failure rate of 110 kV lines. Using empirical data, the authors carried out parametric verification and non-parametric verification of the failure duration, the duration of power outages, and the duration of emergency shutdowns. Based on the obtained data and according to the research conducted by the authors, the average line renewal time at this voltage level is 26.1 h, the average time of emergency outages is 14.1 h, and the average power outage time at the recipients is 4.58 h. It should be emphasized, however, that the results obtained by the authors pertain only to a limited area of Poland, and outage times could vary substantially when considering transmission lines across the entire country. In [47], [PERSON] and [PERSON] focused on determining the failure rate of 110 kV, 220 kV, and 400 kV lines operating in the Croatian power system. The issue of the reliability of 110 kV, 220 kV, and 400 kV lines in Croatia is also discussed in [48], where the authors, based on data from 1995 to 2006, present the impact of regular network maintenance on the reliability of transmission lines. Reliability indicators for transmission lines in the Sub-Saharan African networks are discussed in [49]. The authors determined the SAIFI and SAIDI coefficients based on data from 2004 to 2014. Original methods for determining the reliability coefficient and calculating the unreliability of transmission lines can also be found in [50; 51], where the authors used fuzzy systems to assess reliability indicators. The literature also includes the use of various types of metaheuristic optimization methods [52; 53; 54]. For example, in [54], the authors use Particle Swarm Optimization for this purpose, and in [55], a Genetic Algorithm is used. Some works, such as [56], try to determine the relationship between the general condition of overhead lines (index x) and their failure rate. The authors used the following formula:  
\[\lambda(x)=Ax^{Bxx}+C \tag{1}\]  
where \(A\), \(B\), and \(C\) are constants determined by taking into account historical failure data. In next group of works, the authors used probability distributions to determine the dependencies for the time of failure removal and to examine the reliability of transmission lines. Examples of such works are [57; 58; 59]. In [57], [PERSON] and his team propose a method for calculating the failure rate for 220 kV transmission lines. They focus on taking into account such factors as weather conditions at the time of the recorded failure or in the month of the failure. [PERSON] and [PERSON] [58] use the Markov set method to assess the reliability of complex power systems. Also, in [60; 61], the authors focus on performing a distribution that takes into account the reliability of transmission lines to plan the optimal maintenance schedule. The Markov method for assessing the reliability of a transmission line is also used in [62; 63], where the authors assume that each transmission line operates in a two-state variable weather environment. Moreover, the reliability of transmission lines in a hurricane occurrence in the United States is assessed using the full Markov method. In [64; 65] the Weibull distribution or its variations are used to determine the reliability coefficient of power system elements. In the case of transformers, interruptions in their operation can be planned or forced.