## 3 Material and Methods
### Preparation of the Simulation Model for Research
In the case of estimating the probability density curves, we also observed that for the data from 2017, various approximation methods took a similar shape. It should be noted that the obtained graph has a typical shape of the probability density function of the Weibull distribution. Based on the results obtained, it was possible to determine the shape parameter, which is one of the parameters of the fitted distribution. In the subsequent part of this study, the survival function was estimated directly from continuous survival times using the Kaplan-Meier method. Each interval then contained exactly one event. The survival function is defined as the product of successive probabilities from the intervals [62]:  
\[S_{n}(t)=\prod_{t_{j}\leq t}\left(1-\frac{d_{j}}{r_{j}}\right) \tag{1}\]  
where:  
\(S_{n}(t)\)--estimated survival function,  
\(\prod\limits_{t_{j}\leq t}\)--product symbol,  
\(d_{j}\)--number of events in the period \(t_{j}\),  
\(r_{j}\)--number exposed per period \(t_{j}\). The results of the estimation of the survival function for the examined empirical data are presented in Figure 4.  
By analyzing the above data, we can determine the value of the survival function in a specific time interval. For example, around 140-170 days of work, the survival rate was 90%. Analyzing the graphs of the tested samples, it should be concluded that the occurrence of the second and subsequent failures significantly affected the probability of survival. Its value dropped below 0.5 already within 100 days, while for machines experiencing only 1 failure, it remained at the level of 0.7 even up to the 220 th day. This is valuable information that allows for the identification of machines that potentially pose a threat to the smooth operation of the production process. Selected statistical tests were used to examine the statistical significance of the analyzed data. The results of the significance tests are presented in Table 5.  
Figure 4: Survival function charts for 2017. Source: own study. Analyzing the above results of the significance tests, it should be stated that in the case of comparing the tests concerning failure no. 2, all the tests showed that the results obtained were statistically significant (\(p<0.05\)). Unfortunately, when comparing the samples in terms of subsequent failures, the significance level in the case of the two tests was above \(p=0.05\), which means that it cannot be concluded that the presented differences were statistically significant. The results of comparing the tests allowed us to conclude that both the occurrence of a second failure and the number of days that pass from the inspection to the occurrence of the failure have a significant impact on the course of the survival function. Machines that have only had one failure are more likely to survive than those that have failed again. Similarly, machines whose fault occurrence time is longer than 90 days from the last inspection are characterized by higher survival function values than those where the fault occurred within 90 days of inspection. Moreover, before building the simulation model in FlexSim software, it was decided to make the following assumptions:  
* The line is open on weekdays from 6:00 a.m. to 4:00 p.m. and closed at other times and on Saturdays and Sundays,
* Sheet metal and finished column feet are available in sufficient quantities to process the order,
* The finished poles are loaded for transport one at a time,
* Each machine has an assigned operator who is responsible for operating it,
* Each operator is assigned to one machine,
* Orders are placed for one type of product, so there is no need to change the equipment,
* Orders are fixed and accepted every Monday (150 pcs.) and Wednesday (200 pcs.). Based on the above data and the assumptions made, a simulation model was built in the FlexSim program. The following data and objects were used for this purpose:  
* Source, i.e., the order generator; the arrival times of individual orders were introduced by importing an Excel spreadsheet.