# Classification of Systems and Maintenance Models
## 4 Classification of Maintenance Models  
This section uses hierarchical classification with the ordinal registration of individual sign values. The classification signs include system structure in terms of reliability, type of inspection during maintenance, degree of system restoration for the system rejected at inspection, and external manifestations of system failure. We chose a hierarchical classification because the first three signs have a subordination relationship. We determined the values of classification signs and established a relationship between them, as shown below. _First classification sign._ A sign of the system structure in terms of reliability (\(a=1\): single-component structure; \(a=2\): series structure; \(a=3\): parallel structure; \(a=4\): structure \"\(h\)-out-of-\(q\)\"; \(a=5\): series-parallel structure; \(a=6\): parallel-series structure; \(a=7\): complex structure). As is well known, the maintenance models depend on the system structure concerning reliability [86; 87; 88; 89; 90]. When \(a=1\), the system is considered a single unit; that is, in the case of the rejection of the system based on the inspection results, the entire system is subject to restoration. When \(a=2,\ldots,7\), the system consists of \(q>1\) units, and only the units rejected during the inspection are subject to restoration. We refer to systems with complex reliability structures as systems whose structural functions extend past the first six values of feature \(a\). For instance, systems with a complex reliability structure may change the reliability structure in different modes of operation. Therefore, in the first stage of the classification, we divided the set of maintenance models for inspected systems (\(M_{0}\)) based on sign \(a\) into seven classes: \(M_{1},\ldots,M_{7}\),  
\[M_{0}=\overset{7}{\cup}M_{a} \tag{7}\]  
where \(M_{i}\cap M_{j}=\varnothing\) if \(i\
eq j\). Figure 2a illustrates the classification of maintenance models by sign \(a\). _Second classification sign._ A sign of the type of inspection (\(b=1\): periodic or sequential inspection at corrective maintenance (CM); \(b=2\): periodic or sequential inspection at CBM; \(b=3\): periodic or sequential inspection at predictive or prescriptive maintenance; \(b=4\): continuous condition monitoring at corrective, preventive, condition-based, predictive, or prescriptive maintenance). A corrective maintenance inspection distinguishes only between the operable and inoperable states of a system. This type of inspection is the simplest, but it has a serious disadvantage, the essence of which lies in the fact that CM inspection allows for detecting defects that have accumulated in the system by the time it is carried out and does not provide any confidence in the system's operability in the future. From the perspective of the system operator, the content of CM inspections falls short of fully achieving the goal of maintenance, which is to prevent failures from occurring while the system is being used for its intended purpose rather than simply identifying failures and fixing their effects. Inspection at CBM is more effective because it employs both the functional failure threshold and the replacement threshold, making it possible to reject systems that have already failed, as well as those that may fail in the next operation interval. An inspection at predictive maintenance includes a prognostication of the system's future state by comparing the predicted parameter values with the functional failure thresholds. The use of prognosis-based inspection allows the rejection of systems that will fail in the upcoming operation interval. This type of inspection is in line with the potential goal of maintenance to allow only those systems that will not fail until the next maintenance time point to operate. Prescriptive maintenance goes beyond predictive maintenance because it generates proactive decisions for equipment restoration based on predictive analytics.