# Advancements in Data Analysis for the Work-Sampling Method
## 5 Case Study
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Activity** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** \\ \hline
1. Machining & 38.23 & 63.89 & 58.33 & 58.33 & 63.33 & 56.85 & 54.07 & 21.30 \\
2. Clamping/unclamping the workpiece & 11.49 & 3.33 & 5.00 & 4.17 & 2.78 & 2.22 & 3.33 & 1.85 \\
3. Dimensional control & 1.69 & 3.89 & 4.44 & 2.78 & 5.56 & 5.37 & 3.70 & 1.85 \\
4. Tool movement in the machining position & 0.38 & 0.37 & 0.74 & 0.83 & 0.56 & 0.56 & 0.37 & 0.00 \\
5. Clamping/unclamping of the tool & 1.13 & 0.93 & 0.37 & 0.00 & 0.93 & 0.56 & 0.19 & 0.93 \\
6. Workstation set-up & 6.21 & 0.00 & 0.19 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\
7. Study of working instructions & 6.78 & 0.56 & 0.74 & 0.83 & 0.19 & 0.00 & 0.37 & 0.00 \\
8. Conversation about tasks & 2.07 & 1.48 & 1.11 & 0.56 & 1.85 & 0.19 & 0.93 & 0.00 \\
9. Tool set-up & 6.97 & 4.44 & 6.67 & 6.39 & 5.19 & 4.81 & 4.26 & 0.74 \\
10. Collecting/returning of tools & 2.07 & 0.56 & 1.30 & 0.56 & 0.93 & 1.11 & 1.48 & 1.67 \\
11. Cleaning the machine & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.67 & 19.44 \\
12. Personal needs (toilet, washing, etc.) & 9.79 & 2.96 & 2.41 & 2.22 & 3.52 & 10.00 & 8.15 & 1.48 \\
13. Annotation of work results & 0.00 & 0.00 & 0.00 & 0.56 & 0.00 & 0.19 & 1.67 & 4.81 \\
14. Handover of work & 0.00 & 0.00 & 0.00 & 0.00 & 0.19 & 0.56 & 0.37 \\
15. Waiting for transport & 0.00 & 0.56 & 0.74 & 0.56 & 0.19 & 0.19 & 0.00 & 0.00 \\
16. Waiting for documentation & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\
17. Machine failure & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\
18. Absence from company & 6.21 & 6.11 & 6.11 & 6.11 & 6.11 & 6.11 & 5.56 \\
19. Business meeting & 5.08 & 0.00 & 0.00 & 0.00 & 0.00 & 0.56 & 0.56 & 0.74 \\
20. Power outage & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\
21. Repair of defects & 0.00 & 0.00 & 0.56 & 0.00 & 0.00 & 0.00 & 0.00 \\
22. Private conversation & 1.69 & 9.44 & 9.63 & 14.44 & 7.59 & 9.26 & 10.56 & 12.04 \\
23. Private absence from the workplace & 0.19 & 1.48 & 2.22 & 1.11 & 1.30 & 1.85 & 2.04 & 27.22 \\ _Productive work_ & **52.92** & **72.41** & **68.89** & **66.11** & **73.15** & **65.56** & **61.67** & **25.93** \\ _Losses_ & **47.08** & **27.59** & **31.11** & **33.89** & **26.85** & **34.44** & **38.33** & **74.07** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Activity proportions by workday hours (in %). The time allowance factor (\(TA_{f}\)) is calculated according to Equation (4):  
\[TA_{f}=\frac{750}{2504+300+577}=0.22\]  
The accuracy achieved for the proportion of productive work is \(\pm 2.51\%\) and for losses is \(\pm 3.86\%\). The lower and upper limits within which the actual shares of productive work are distributed are \(59.1\%\) to \(62.1\%\), and \(37.9\%\) to \(40.9\%\) for losses. As already mentioned, the calculation of Pearson's correlations between the activity proportions by workday hours represents a procedural enhancement of the analysis of the results of the work-sampling method. The correlations between all pairs of activities were calculated according to Equation (5) and are shown in Table 4; all values were multiplied by \(10\) and rounded (we have values between \(-9\) and \(+9\)). Activities whose hourly shares never exceed \(1\%\) are not considered in the correlation analysis. Satisfactory accuracy of the result is not guaranteed for these activities, as already described in Section 2 (in the description of the disadvantages of the work-sampling method) and at the end of Section 4. The excluded activities can be found under reference numbers 4, 14, 15, and 21. Discussion  
When analyzing potential dependencies between activities, we must consider pairs that have a value less than \(-6\) or greater than \(6\), bolded in Table 4. There are \(27\) such correlations (without excluded activities):  
* Machining and absence from the company (7)--we cannot confirm the connection (false correlation).