# Classification of Systems and Maintenance Models
## 3 Classification of Systems
Definitions of the achieved and inherent availability for repairable systems are available in many references, such as examples [81; 82]. Since subgroups \(I_{2511}\) and \(I_{2512}\) include non-repairable systems, we define the achieved and inherent availability for them. The achieved availability of a non-repairable system is the ratio of the mathematical expectation of the time the system is in an operable state for a certain period of operation to the sum of the mathematical expectations of the time the system is in an operable state and downtime owing to unrevealed failures, scheduled and unscheduled maintenance (checks and removals). The inherent availability of a non-repairable system is formulated in the same manner as that of a repairable system. However, when calculating the inherent availability, because there is no repair, only the characteristics of the operable and unrevealed failure states and unscheduled removals are considered. Figure 1 shows the hierarchical classification of the systems, which includes two classes, six subclasses, nine groups, and thirteen subgroups of systems. The corresponding maintenance effectiveness indicators are listed in Table 1. Table 1 uses the following notations: \(P_{O}\) is the OPFFO, \(C^{r}\) is the UC for a repairable system, \(A_{ma}\) is the mission availability, \(A_{a}^{r}\) is the achieved availability for a repairable system, \(W^{r}\) and \(V^{r}\) are the AOPUT and AMCUT for a repairable system, respectively, \(A_{i}^{r}\) is the inherent availability for a repairable system, \(P_{A}\) is the APFFO and \(C^{n}\) is the UC for a non-repairable system, \(A_{a}^{n}\) is the achieved availability for a non-repairable system, \(A_{i}^{n}\) is the inherent availability for a non-repairable system, and \(W^{n}\) and \(V^{n}\) are the AOPUT and AMCUT for a non-repairable system, respectively. The index \"1\" in the designation of indicators \(C^{r}\), \(W^{r}\), \(V^{r}\), \(C^{n}\), \(W^{n}\), and \(V^{n}\) indicates that the mode of the system use is continuous, and therefore, when calculating indicators, it is necessary to consider losses due to downtime during scheduled maintenance and unscheduled repairs (for repairable systems). Index \"2\" in the designation of these indicators specifies intermittent use of the system. In this case, losses owing to downtime during scheduled maintenance were not considered. The maintenance effectiveness indicators listed in Table 1 characterize the most significant signs of the design, purpose, and operating conditions of the system. Therefore, they should be considered as key indicators. When solving maintenance optimization problems, additional indicators that specify the specifics of the situation under consideration can be included in the number of indicators characterizing maintenance effectiveness. **Example 1**. : _We determined the maintenance effectiveness indicators for an aircraft instrument landing system (ILS), which is the most common radio navigation instrument approach system in aviation._  
Redundant electronic systems make up modern digital avionics [83]. The onboard ILS is an avionics system. Any avionics system usually comprises two or three identical line-replace units (LRUs) [84]. Avionics LRUs have a reputation for their excellent testability and maintainability standards. Shop-replaceable units (SRUs) are LRU interchangeable parts. Typically, an SRU is a printed circuit board assembly that may be changed or repaired in a workshop. ILS is therefore a repairable system (\(i=1\)). System failures during the descent and landing phases can lead to dangerous situations. Therefore, the ILS system was not included in the master minimum equipment list (MMEL) [85], which listed onboard systems in an aircraft that can be classified as having little to no effect on the safety of the operation. Hence, the failure consequence is the nonfulfillment of the critical functions (\(j=1\)). Economic assessment of the consequences of failure is impossible (\(k=1\)).