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Logistics processes, their effective planning as well as proper management and effective implementation are of key importance in an enterprise. This article analyzes the process of supplying raw materials necessary for the implementation of production tasks. The specificity of the examined waste processing company requires the knowledge about the size of potential deliveries because the delivered waste must be properly managed and stored due to its toxicity to the natural environment. In the article, hidden Markov models were used to assess the level of supply. They are a statistical modeling tool used to analyze and predict the phenomena of a sequence of events. It is not always possible to provide sufficiently reliable information with the existing classical methods in this regard. Therefore, the article proposes modeling techniques with the help of stochastic processes. In hidden Markov models, the system is represented as a Markov process with states that are invisible to the observer but with a visible output (observation) that is a random state function. In the article, the distribution of outputs from the hidden states is defined by a polynomial distribution.

The quality and reliability of consumables, including gear oils, results in the failure-free operation of the transmission components in heavy trucks. It is known that oil viscosity is essential for all lubricated tribopairs for wear and friction reduction in all vehicles with a gearbox. Viscosity may be influenced by the contamination that wear products can impart on the oil. Oil contamination can also affect lubrication efficiency in the boundary friction conditions in gearboxes where slips occur (including bevel and hypoid gearboxes). The present research focused on this issue. An obvious hypothesis was adopted, where it was theorized that exploiting the contaminants that are present in gear oil may affect how the lubricating properties of gear oils deteriorate. Laboratory tests were performed on contaminants that are commonly found in gear oil using the Parker Laser CM20. The study was designed to identify a number of different solid particles that are present in oil. At the second stage, friction tests were conducted for a friction couple “ball-on-disc” in an oil bath at 90 °C on a CSM microtribometer. The quantitative contamination of the gear oils that contained solid particles and the curves representing the friction coefficients of fresh oils with a history of exploitation were compared. The test results were statistically analysed. Exploitation was shown to have a significant impact on the contamination of gear oils. It was revealed that the contamination and the mileage had no effect on the tested oils.

This article uses Markov and semi-Markov models as some of the most popular tools to estimate readiness and reliability. They allow to evaluate of both individual elements as well as entire systems—including production systems—as multi-state structures. To be able to distinguish states with varying degrees of technical readiness in complicated and complex objects (systems) allows to determine their individual impact on the tasks performed, as well as on the total reliability. The application of the Markov process requires, for the process dwell times in the individual states, to be random variables of exponential distribution and the fulfilling Markov’s property of the independence of these states. Omitting these assumptions may lead to erroneous results, which was the authors’ intention to show. The article presents a comparison of the results of the examination of the process of non-parametric distribution with an analysis in which its exponential form was (groundlessly) assumed. Significantly different results were obtained. The aim was to draw attention to the inconsistencies obtained and to the importance of a preliminary assessment of the data collected for examination. The diagnostics of the machine readiness operating in the studied production company was additionally performed. This allowed to evaluate its operational potential, especially in the context of solving process optimization problems.