In this paper, an assessment of the failure frequency of machines in a series-parallel structure was conducted. The analyses contain the decomposition of the system according to the general theory of complex systems. Based on the results obtained, a model for an optimal determination of the mean time to failure (MTTF) according to the expected value of the gamma distribution was proposed. For this purpose, the method of moments was used to determine the optimal values of the parameters of the estimated gamma distribution. The article is designed to be analytical. The object of consideration in this analysis is the real production system working in accordance with make-to-order, with a high degree of product customisation. Moreover, in the considered system occurs a dichotomy of mutually exclusive flows: push and pull. In the article, the main emphasis was placed on the applicability of the proposed MTTF value-shaping algorithm. Then, the maintenance strategy for each machine (reactive, preventive or predictive) was proposed. Maintenance strategy selection considered sustainable development principles in the criterion of minimizing maintenance actions, fulfilling the assumption of not interrupting the flow of the processed material. Based on inductive analyses, the concepts of improvement actions individually for each machine in the analysed subsystem were deductively defined. As a result, it was proved that a reactive maintenance strategy is appropriate for machines that have manufacturing reserves and are low priority. The equipment possessing manufacturing reserves but also having an impact on the risk of interrupting the flow of the processed material should be operated in accordance with a preventive maintenance strategy. A predictive maintenance strategy was proposed for the machines with the highest priority, which simultaneously do not have manufacturing reserves and the risk of manufacturing line operation interruption is high. The considerations were conducted with a holistic approach, taking into account the main functional areas of the enterprise.

In this paper, the concept of hybrid predictive maintenance for a single industrial machine is presented. A review of the solutions in the area of machine maintenance (especially predictive maintenance) which have been described in the literature is provided. The assumptions of the hybrid predictive maintenance model for modules, machines, or systems are presented. The methods used within the developed methodology are described. This includes the use of diagnostic data, experience, and a mathematical model. A case study of an industrial machine on which a system for collecting diag-nostic data has been pilot-implemented, using, among others, vibration sensors and drive system pa-rameters for damage detection is presented. The registered data can be used to precisely determine the time of upcoming failure after detection of the characteristic symptoms resulting from component wear In addition, an analysis of the durations of correct operation and failure events was performed and indicators describing these values were determined. The values of the aforementioned indicators were determined based on empirical data and described using a gamma distribution. The objective of the research was to prepare, implement and draw conclusions on a hybrid predictive maintenance model. A real industrial machine was used in the research study. The hybrid predictive maintenance model presented in this paper enables the use of data of different types (diagnostic, historical and mathemat-ical model-based) in scheduling machine downtime for maintenance actions. On the basis of the re-search conducted, it was determined which machine operating parameters are characterised by varia-bility that enables the detection of upcoming failure. This allows for precise planning of maintenance activities and minimization of unplanned downtime.

This paper analyses the disruptions occurring in a production system determining the operating states of a single machine. A system with a convergent production character, in which both single flows (streams) and multi-stream flows occur, was considered. In this paper, a two-level formalisation of the production system (PS) was made according to complex systems theory. The continuity analysis was performed at the operational level (manufacturing machine level). The definition of the kth survival value and the quasi-coherence property defined on chains of synchronous relations were used to determine the impact of interruption of the processed material flow on uninterrupted machine operation. The developed methodology is presented in terms of shaping the energy efficiency of technical objects with the highest power demand (the furnace of an automatic paint shop and the furnace of a glass tempering line were taken into consideration). The proposed methodology is used to optimise energy consumption in complex production structures. The model presented is utilitarian in nature—it can be applied to any technical system where there is randomness of task execution times and randomness of unplanned events. This paper considers the case in which two mutually independent random variables determining the duration of correct operation $T_P$ and the duration of breakdown $T_B$ are determined by a given distribution: Gaussian and Gamma family distributions (including combinations of exponential and Erlang distributions). A formalised methodology is also developed to determine the stability of system operation, as well as to assess the potential risk for arbitrary system evaluation parameters.

The objective of this article is to analyse and evaluate the effectiveness of predictive maintenance for machines performing key functions within a production structure. This article presents a methodology for determining the Equipment Priority Number (EPN), calculated based on parameters such as energy consumption, the criticality of machines in the value stream, and their impact on the continuity of the supply chain. The experimental implementation of a system for monitoring operational parameters—including current consumption, vibrations, and torque moments—enabled the prediction of potential failures and the planning of maintenance actions, which contributed to improving operational stability and reducing the risk of unplanned downtime. The obtained results confirm the effectiveness of the proposed methodology and demonstrate that a predictive maintenance system supported by the EPN indicator enables accurate prioritisation of maintenance activities in an actual production system. The findings also show that implementing the EPN algorithm allows for more precise prioritisation in highly customised production environments. Furthermore, the analysis of the collected data suggests the potential for further optimisation through the integration of data-driven diagnostics and artificial intelligence methods, which could enhance the efficiency and competitiveness of the system. This study’s conclusions provide a foundation for advancing predictive maintenance methods in industrial production.