# Classification of Systems and Maintenance Models
The same effectiveness indicators were used for diverse types of maintenance, including preventive, corrective, condition-based, predictive, and prescriptive maintenance. Simultaneously, there is no formal classification of maintenance models that allows an appropriate model to be objectively chosen according to certain features. 6. There is no formalized approach to the classification of systems for selecting maintenance effectiveness indicators and for the classification of the maintenance models necessary to calculate the selected indicators. * In the existing preventive, corrective, condition-based, and predictive maintenance models, it is assumed that failures are detected using periodic (or sequential) inspections and/or continuous condition monitoring. * Prescriptive maintenance uses condition monitoring and artificial intelligence to track a larger range of data and predict when maintenance is necessary in real-time. In this study, we propose a classification of technical systems that allows us to select maintenance effectiveness indicators depending on signs such as system maintainability, failure consequences, an economic assessment of the failure consequences, and a temporary mode of system use. This classification makes it possible to identify 13 subgroups of indicators, including most of the known indices and some new ones. The study also proposes a classification of maintenance models to calculate each maintenance effectiveness indicator. The developed classification allows the selection of a maintenance model depending on features such as the system structure in terms of reliability, type of inspection, degree of the system's restoration, and external manifestations of failure. This classification makes it possible to identify one hundred and sixty-eight subgroups of the maintenance models. We illustrate how to determine the maintenance effectiveness indicators for a subgroup of maintenance models, which assume that the system has a single-component structure, that the type of inspection is similar to CBM, that the perfect repair is used, and that only hidden failures occur in the system. We developed mathematical maintenance models for the case of an arbitrary distribution of time-to-failure and multiple imperfect inspections, where the probabilities of correct and incorrect decisions depend on the time of inspection and failure occurrence. A numerical example illustrates the determination of the optimal number of inspections for a particular stochastic degradation process in condition-based and corrective maintenance. The remainder of this article is organized as follows: Section 2 provides a review of the classification of maintenance effectiveness indicators and maintenance models. The classification of technical systems for selecting maintenance effectiveness indicators is discussed in Section 3. Section 4 presents the classification of the maintenance models. Section 5 develops the condition-based maintenance model and provides formulas for calculating maintenance effectiveness indicators. In Section 6, an example of deterioration process modeling is considered. The results are outlined in Section 7, followed by a discussion in Section 8. Section 9 presents the conclusions and potential future work. Abbreviations and references are provided at the end of this article.