## 3 Case Study. The Applied Evaluation Processes
### Phase 4: Improvement  
In this phase, two methods that can help to improve the reliability of the human-machine system in the machine tool area are applied. These methods depend on the type of origin of the failures that occurred and their effect on the system's reliability. Failures were analyzed to identify their origin. A case study was used for this purpose, so the data that appear were obtained from a machine shop. Origin and contribution of failures. The analysis consists of a classification of kinds of failures by origin using a cluster analysis to detect the kinds of origins of failures in the machine tool area according to similar characteristics of each identified failure that occurred in the machine tool. Table 5 shows this classification. Table 5 shows that the failure origins identified were mechanical, human error, heat treatment, material, and unexpected event and that failures of a mechanical origin were most common in the machine tools. The frequency of each kind of failure by origin is presented in Table 6. Through the Pareto Diagram shown in Figure 5, we identified the sources of failure that most affected their appearance and made the greatest contribution to or had the highest impact on the \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Mechanical** & **Mechanical** & **Mechanical** & **Human Error** & **Heat Treatment** & **Material** & **Unexpected Event** \\ \hline
3 & 15 & 31 & 1 & 43 & 26 & 42 \\
4 & 18 & 35 & 2 & 49 & 30 & 45 \\
5 & 19 & 37 & 10 & 50 & 33 & \\
6 & 20 & 38 & 16 & 51 & 34 & \\
7 & 21 & 40 & 17 & 52 & 58 & \\
8 & 22 & 41 & 27 & 53 & & \\
9 & 23 & 46 & 32 & 55 & & \\
11 & 24 & 47 & 36 & 56 & & \\
12 & 25 & 48 & 39 & 57 & & \\
13 & 28 & & 44 & & & \\
14 & 29 & & 54 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Classification of kinds of failure by origin. reliability of the man-machine system. Table 6 shows that the origin with the highest number of failures is the mechanical type, with 31 out of 58 (53.54%). Using data from Table 6, a Pareto Diagram of the origins of failures and their contribution from Figure 5 was drawn. In Figure 5, failures of mechanical and human-error origin are vital causes, with 72.4% of the contribution. In contrast, failures of heat treatment, material, and other origin were identified as trivial causes, with a 27.6% contribution to the failures in the products of the machine tool area. After identifying that the failures of both mechanical and human-error origin contribute most to the appearance of failures in the products, two improvement methods, namely monitoring the parameters \(\beta\) and \(\eta\) of the Weibull distribution for time-dependent failures, such as those of a mechanical origin, and monitoring the parameter \(\lambda\) of the exponential distribution for non-time-dependent failures, were developed. Monitoring of Parameters between Two Sequential Periods  
The objective of monitoring the parameters is to identify the lowest reliabilities in the human-machine system during two sequential periods. A case study from a machine shop was carried out to develop this method. The steps were as follows:  
Component-subsystem relationships present in failures. This refers to the time to failure generated by a specific component-subsystem combination from a data distribution, either Weibull or exponential, with their corresponding parameters. Tables 7 and 8 show the parameters for each component-subsystem relationship presented in the failure analysis for the period from 25 January to 30 January 2021 and for the period from 17 May to 28 May 2021, respectively. These parameters were helpful in evaluating the reliability of each component-subsystem relationship and they were obtained using the software Weibull ++.