# Classification of Systems and Maintenance Models
## 3 Classification of Systems
Therefore, in the first stage of the classification, the initial set of systems \(I_{0}\) is divided according to sign \(i\) into the class of repairable systems \(I_{1}\) and the class of non-repairable systems \(I_{2}\), that is,  
\[I_{0}=I_{1}\cup I_{2} \tag{1}\]  
moreover \(I_{1}\cap I_{2}=\varnothing\), where \(\cup\), \(\cap\), and \(\varnothing\) are symbols denoting the union and intersection of subsets, and an empty subset, respectively. Figure 1a illustrates the classification of systems by sign \(i\). _Second classification sign._ A sign of failure's consequences \(j\) (\(j=1\): the fact that the system does not perform a safety-critical function assigned to it in a given volume, \(j=2\): the fact that the system does not perform a safety-critical function assigned to it in a given volume at an arbitrary moment of beginning the \"operation mode,\" \(j=3\): downtime of the  
Figure 1: Hierarchical classification of systems for the selection of maintenance effectiveness indicators: (**a**) classification of systems into repairable and non-repairable; (**b**) classification of repairable systems; (**c**) classification of non-repairable systems. system in a state of unrevealed failure when used as intended and downtime associated with scheduled maintenance and unscheduled repair; \(j\) = 4: downtime of the system in a state of unrevealed failure when used as intended, regardless of the downtime associated with scheduled maintenance; \(j\) = 5: downtime of the system in a state of unrevealed failure when used as intended and downtime associated with unscheduled system replacement). When evaluating the consequences of a failure, the sign value of \(j\) = 1 corresponds to the case in which the consequences affect safety. According to the European Standard ECSS-S-ST-00-01C--Glossary of Terms [78], \"a safety-critical function is the function that, if lost or degraded, or as a result of incorrect or inadvertent operation, can result in catastrophic or critical consequences.\" When \(j\) = 2, the system can be either in standby mode or operation mode, and when it is in operation mode, it does not perform a safety-critical function. In the standby mode, the system is accessible for inspection and repair. The system must operate without failure for a predetermined time in the operating mode, where failure affects safety. Maintenance and inspection were not performed in the operating mode. The sign value \(j\) = 3 corresponds to the case when material damage due to a failure is caused by both the system's downtime in a state of unrevealed failure during operation and by the downtime due to the restoration. The sign value \(j\) = 4 corresponds to the case in which the material damage owing to a failure is much greater than the losses caused by the system downtime. In this case, as a rule, the system downtime owing to restoration work does not lead to substantial material loss. If it is impossible to estimate material losses due to system failure, the value \(j\) = 4 corresponds to the case in which either scheduled maintenance or restoration of the system, or both, can be carried out during time intervals when the system is not used. The sign value \(j\) = 5 corresponds to the operation of a non-repairable system, the consequences of which do not affect safety. The sign values \(j\) = 2, 3, and 4 correspond to the cases of operation of repairable systems, and when \(j\) = 1, the system can be both repairable and non-repairable. Therefore, in the second stage of the classification, we divided class \(I_{1}\) into four subclasses: \(I_{11}\), \(I_{12}\), \(I_{13}\), and \(I_{14}\), and class \(I_{2}\) into two subclasses: \(I_{21}\) and \(I_{25}\), that is,  
\[I_{1}=\mathop{\cup}\limits_{j=1}^{4}I_{1j} \tag{2}\]  
\[I_{2}=I_{21}\cup I_{25} \tag{3}\]  
Figure 1b,c illustrates the classification of systems by sign \(j\). _Third classification sign._ A sign of the economic evaluation of failure consequences \(k\) (\(k\) = 1: economic evaluation is impossible; \(k\) = 2: economic evaluation is possible).