## 1 Introduction
The implementation of appropriate preventive and repair strategies allows the reduction of system maintenance costs. Such strategies include the replacement of important system components and setting the frequency of inspections to determine the technical condition. The schedule on which we base our activities is often set by the designer or manufacturer of the system. Under operating conditions after the end of the warranty, this schedule is usually upgraded by users. They are often the ones who decide about the replacement of worn elements. CM actions always require a prior identification and diagnosis of the damage, so they are expensive and require high personnel skills. The costs of preventive maintenance, PM, are lower than the costs of CM repairs. A similar relationship is also found for average repair times and preventive maintenance. For some systems, it is possible to repair a failed component without replacing it. This action can be called minimal repair (MR). Minimal repair consists of restoring the current state of the object to its state before the damage occurred. Looking at it in this way can be considered minimal repair. This logic allows the construction of new practical models of replacements with minimal repair. The indicated reasons confirm that this is an important research topic in reliability engineering. Strategies for preventive actions that propose optimal decision-making models will reduce the cost of system maintenance and the risk of adverse events. The problem is the high maintenance costs of agricultural machinery. For this reason, the PM strategy was established. The PM issues are described in [4]. The article evaluates the impact of the PM strategy on the reliability indicators (failure rate, mean time between failures (MTBF), mean time to repair (MTTR) and mechanical availability) of a rice harvester. These reliability rates have been calculated for each month of the harvesting season over 3 years. The unfavorable results prompted the authors to propose a new PM strategy, condition-based maintenance (CBM). The results of this proposed strategy showed improvements in various reliability metrics. The models for preventive maintenance, due to their economic importance, have aroused growing interest in the studies of systems reliability. [PERSON], in [5], introduced the concept of minimal repair. It deals with a repair model with a monthly income generated for the tested technical object as a criterion function. For this purpose, he used queuing theory, not reliability. In the field of reliability theory, the concept of minimal repair was used by [PERSON] and [PERSON] [6]. They presented a model for periodic replacements and minimal repair. This model assumes that, after each minimal repair, the damaged technical system is restored only to the same state as before the damage. The first formal definition appears in a scientific article by [PERSON] and [PERSON] [7]. In their article, [PERSON] and [PERSON] [8] also raise the issue of minimal repair in the event of damage to a technical object. Assuming the probability is \(\mathrm{p}\) for a perfect repair, for a minimal repair, the probability is \(\mathrm{q}=1-\mathrm{p}\). Further work by their team led [PERSON] and [PERSON] [9] to propose a new version. In this assumption, the object is replaced with a new one after time T, and a perfect repair or minimal repair is carried out with probabilities \(\mathrm{p}\) and \(\mathrm{q}\), respectively, for intermittent failures. The approach to the problem in [8] assumes that the probability of a thorough repair depends on the age of the technical object at the time of failure. The minimum repair model in the available literature is built using various mathematical methods. In articles [10; 11], we will find an overview of the methods used to build the criterion functions for minimal repair models with preventive maintenance by age. A more comprehensive and up-to-date overview of minimal repair work is available in [12].