*3.1. Description of the Company Studied*

The subject of the research is a company manufacturing plastic garbage bags. It is a three shift serial production, with 8-h shifts. The roller welding machines, which weld and perforate finished rolls of polyethylene film, constitute a critical element of the whole process. Among all the machines in the production line, the efficiency of the roller welding machines is the lowest, they have the highest failure rate and their downtimes lead to substantial increase in costs, making them a bottleneck in the process. This is why they became the subject of the study. The analysis was carried out on the example of a selected model, marked with the H2 symbol.

The analysis of the activities carried out when operating the roller welding machines allowed to distinguish the states of the machine. They are presented in the Table 1.



Among the selected states, those directly related to the production process should be distinguished: S1—manufacturing process, S4—necessary maintenance activities to keep the machine in good working order and to prepare it for the manufacturing process. Planned employee breaks, resulting from the Labor Code (S5), also constitute a necessary element of the manufacturing process. Other states should be identified as undesirable. These include the stoppage in the manufacturing process, due to lack of orders, S3, and lack of raw materials, S6.

The relationships between the individual states are shown in Figure 1.

**Figure 1.** Diagram of the inter-state transitions of the process studied.

#### *3.2. Studying Markov's Property*

In the first stage, the lack of memory characteristic of the process was assessed. The goodness of fit test χ<sup>2</sup> was used for the study, defining at the level of significance α = 0.05 the zero hypothesis assuming that the chain studied meets the Markov property, and the alternative hypothesis that the Markov property is not met [11]. The test statistic χ<sup>2</sup> = 228.7, while related to it *p*-value = 0.264, which means that there are no grounds to reject the zero hypothesis on the chain meeting the Markov property.
