## 1 Introduction  
The paper focuses on the reliability of steel plane trusses under fire conditions with the fully probabilistic model. Therefore, it combines two important issues: structural reliability and design of the structure under fire conditions. The theory of reliability analysis is now well established; there are numerous methods that can be enumerated, including, amongst others: approximation methods (FORM, SORM) [1; 2; 3; 4], simulation methods (Importance Sampling, Monte Carlo) [5; 6; 7; 8], artificial neural networks [9; 10], Stochastic Finite Element Method (SFEM) [11; 12], Adaptive Response Surfaces [13; 14], or System Reliability Analysis [15; 16; 17; 18]. The interesting approach to the management of reliability and predicting the service life of the structure is to use Markov chains [19; 20; 21]. All mentioned methods are widely used in many branches of technical sciences to assess the reliability of elements or structures. The reliability index of an element or structure defines its safety and can be assumed to be an alternative to a partial safety factor. The reliability index \(\beta\) is defined as follows:  
\[\beta=-\Phi^{-1}\Big{(}P_{f}\Big{)} \tag{1}\]  
where \(P_{f}\)--probability of failure,  
\(\Phi\)--Laplace function. In the paper, the authors computed the reliability of the structure using the SYSREL program [22], where the system reliability can be combined with approximation or simulation methods. The part related to obtaining the temperature of the elements and the response of the structure under fire conditions was carried out according to Eurocode [23; 24]. Many scientists focus on the reliability aspects of the structure in fire conditions. A few years ago, the probability of failure began to be considered as an alternative to the partial safety factor for the structure in accidental design situations, when a fully developed fire occurs in the building compartment [25]. One of the interesting but difficult and very wide topics is preparing fire scenarios [26; 27]. Another noteworthy problem is the reliability of fire protection coatings [28]. In the following article, neither fire (fire scenarios) nor coating reliability of coatings was considered. It was assumed that the structure is under the influence of a fully developed fire and that the material characteristics of the fire protection coating are deterministic. The response of the structure under fire conditions can be very different depending on many factors. This issue with the assessment of the reliability of steel columns under fire according to the US prescriptive is discussed in [29]. The next important issue is the probabilistic character of the properties of the steel strength [30]. In [31], a comparison of different reliability methods to assess the safety of steel trusses is discussed. Both statically determinate and indeterminate structures are analyzed and the validity of system reliability analysis is demonstrated. The presented paper focuses on the system reliability of steel structures under fire conditions. In fact, system reliability analysis, searching failure modes, or building failure paths were previously considered in many scientific works. Unfortunately, most of them are related to quite simple structures or are limited to local failure [32; 33]. There are some publications about different strategies for finding failure modes in the case of large structures. [PERSON] and [PERSON] [34] reviewed typical methods, i.e., the incremental loading method, the branch-and-bound technique, or \(\beta\)-unzipping method. They also proposed a new selective procedure combined with a genetic algorithm. [PERSON] [35] proposed a variant of the non-dominated sorting genetic algorithm used for multi-objective reliability optimization of series-parallel systems. The other method is the gradient tree boosting algorithm, which enables the user to evaluate the safety of steel trusses [36].