## 1 Introduction
The cost related to a single component of the system is defined as the cost, i.e., the cost of production downtime and the cost of repairs through the following equation:  
\[S_{i} =\mathrm{W}_{s}\cdot t_{i}\cdot L_{i}+\mathrm{K}_{i} \tag{2}\]  
where \(S_{i}\) represents the cost tied to the \(i\)-th component, \(W_{s}\) the value of the unit loss in the system downtime state, \(t_{i}\) the time needed for the component to be fixed, \(L_{i}\) the the amount of unit losses and \(K_{i}\) the cost of repairs. The estimate of the frequency of faults is made on the basis of data on previous faults; therefore, it cannot be considered reliable. In addition, information from equipment manufacturers is often unavailable or difficult to use in a real work environment. From a security point of view, it is necessary to use a different and more complex data analysis than the one shown. Special attention should be paid to distinguishing between the individual system components in terms of exposure to risk, as a small number of components significantly affects the amount of the overall risk. In modern technical facilities and enterprises, CBM has become a leading maintenance strategy in contrast to more traditional solutions relying on time-based maintenance. An optimal CBM strategy has the potential to provide significant benefits, increasing system availability, reducing maintenance costs and increasing product quality. A literature review [9] provides a detailed insight into theoretical foundations, specific implementations and operational aspects as well as future research directions. Theoretical and practical development in the field of general CBM and its current state of the art are in detail presented [10] and acknowledged. The condition assessment is of great importance for the oil immersed type power transformers. Several methods for assessment of key parameters of the power transformer are well established and documented. They can be divided into two major groups, offline methods and online methods, each consisting of specific methods [14; 15]. Common offline methods are determination of the degree of polymerization (DP), furan analysis, dielectric response analysis, insulation resistance, sweep frequency response analysis (SFRA) and others [11; 16]. Online methods are dissolved gas analysis (DGA), partial discharge analysis, thermal monitoring and vibration analysis [11; 15; 17]. DGA is the most widely applied technique in modern monitoring systems and the application can be achieved either online or offline. After offline or online measurement and data acquisition procedures, several methods can be used in order to determine overall condition or state of power transformer [16; 18; 19]. Described methods may include complex computational and/or artificial intelligence methods [12; 13; 19; 20; 21] (machine learning, artificial neural networks, fuzzy logic, etc.). However, existing methods are often limited with the input information, their focus on a specific data set, their inability to assess the overall condition of the power transformer and a lack of the possibility to handle incomplete or uncertain data. The solution presented in this paper proposes condition-based assessment and maintenance based on multiple attribute analysis and an evidential reasoning algorithm. The first step is to perform a decomposition of a desired object from general up to elementary attributes, determine weights for all attributes, collect offline and online data, convert collected quantitative data to qualitative grades, perform an aggregation process with attribute grades, weights and uncertainty and finally, obtain a single value, which represents the current condition state of the observed object. This utility grade is essential for a decision-making process regarding maintenance. This paper is structured into four sections. Section 1, the Introduction, presents the current state of the CMB and power transformer maintenance procedures.