# Evaluation of the Variability of Vibration Measurement Results in Rolling Bearing Quality Control
## 4 Results and Discussion
In the case of results obtained in the medium frequency band, more similar arithmetic means of vibration levels were received for systems 2 and 3, whereas in the high frequency band, more similar results were received for systems 1 and 2. It is also possible to note the lack of consistency for the maximum and minimum values indicated by the systems. The value chronology of the obtained results also differs depending on the analysed band. However, it is difficult to \begin{table}
\begin{tabular}{l c c c} \hline
**Measurement System No.** & **1** & **2** & **3** \\ \hline number of measurements & & 50 & \\ arithmetic mean, And & 6.98 & 6.84 & 7.56 \\ mean squared deviation of single measurement, & 0.29 & 0.24 & 0.21 \\ minimum value, And & 6.4 & 6.2 & 7.1 \\ maximum value, And & 7.6 & 7.3 & 8.1 \\ spread, And & 1.2 & 1.1 & 1 \\ final result of single measurement, And (\(p\) = 0.95) & \(6.98\pm 0.57\) & \(6.84\pm 0.48\) & \(7.56\pm 0.41\) \\ data spread skewness coefficient & 0.09 & \(-0.44\) & \(0.1\) \\ data spread kurtosis & \(-0.51\) & \(-0.04\) & \(-0.03\) \\ statistic \(\chi^{2}\); critical value \(\chi_{\text{kr}}{}^{2}\) (\(p\) = 0.95) & \(0.37\); \(5.99\) & \(1.76\); \(5.99\) & \(0.43\); \(3.84\) \\ \hline \end{tabular}
\end{table} 
Table 4: Spread parameters for a series of measurements of the vibration’s RMS value for rolling bearing type 6205 in the 1800–10,000 Hz frequency band on three different systems. \begin{table}
\begin{tabular}{l c c c} \hline
**Measurement System No.** & **1** & **2** & **3** \\ \hline number of measurements & & 50 & \\ arithmetic mean, And & 6.02 & 4.6 & 5.26 \\ mean squared deviation of single measurement, & 0.3 & 0.22 & 0.23 \\ And & 5.6 & 4.3 & 4.9 \\ maximum value, And & 6.9 & 5 & 5.7 \\ spread, And & 1.3 & 0.7 & 0.8 \\ final result of single measurement, And (\(p\) = 0.95) & \(6.02\pm 0.59\) & \(4.6\pm 0.42\) & \(5.26\pm 0.44\) \\ data spread skewness coefficient & 1.02 & 0.1 & 0.11 \\ data spread kurtosis & 0.37 & \(-1.19\) & \(-0.94\) \\ statistic \(\chi^{2}\); critical value \(\chi_{\text{kr}}{}^{2}\) (\(p\) = 0.95) & \(10.36\); \(5.99\) & \(10.13\); \(9.49\) & \(9.56\); \(5.99\) \\ \hline \end{tabular}
\end{table} 
Table 2: Spread parameters for a series of measurements of the vibration’s RMS value for rolling bearing type 6205 in the 50–300 Hz frequency band on three different systems. \begin{table}
\begin{tabular}{l c c c} \hline
**Measurement System No.** & **1** & **2** & **3** \\ \hline number of measurements & & 50 & \\ arithmetic mean, And & 6.27 & 5.66 & 5.38 \\ mean squared deviation of single measurement, & 0.28 & 0.35 & 0.42 \\ minimum value, And & 5.8 & 5.1 & 4.7 \\ maximum value, And & 6.8 & 6.3 & 6.1 \\ spread, And & 1 & 1.2 & 1.4 \\ final result of single measurement, And (\(p\) = 0.95) & \(6.27\pm 0.56\) & \(5.66\pm 0.68\) & \(5.38\pm 0.83\) \\ data spread skewness coefficient & 0.12 & \(-0.06\) & 0.21 \\ data spread kurtosis & \(-0.65\) & \(-0.91\) & \(-0.96\) \\ statistic \(\chi^{2}\); critical value \(\chi_{\text{kr}}{}^{2}\) (\(p\) = 0.95) & \(5.08\); \(5.99\) & \(5.75\); \(5.99\) & \(7.35\); \(7.81\) \\ \hline \end{tabular}
\end{table} 
Table 3: Spread parameters for a series of measurements of the vibration’s RMS value for rolling bearing type 6205 in the 300–1800 Hz frequency band on three different systems. The test \(\chi^{2}\) conducted individually for each system and frequency band demonstrated that there is no reason not to treat the spreads obtained in the medium and high frequency bands as normal. The result of test \(\chi^{2}\) in the low frequency band for all systems also demonstrated that the measurement data are not distributed according to a normal spread. It is possible that the mechanical arrangement specific to each system distorts the spread of the obtained results in the low frequency band. Each design interferes with the results in a different way.