## 5 Discussion
Although the Weibull distribution for B = 1 mimics the exponential distribution, both distributions are different and behave differently. This fact is due to the Weibull distribution being generated by a non-homogeneous Poisson process in which the risk depends on time, and the exponential distribution is based on a Poisson process in which the risk does not depend on time (a lack of memory property). Based on this fact, we used the Weibull distribution for components and subsystems whose failure mode is mechanical. Due to the mechanical stress that accumulates damage over time, the failure risk depends on time as in the Weibull distribution (or the non-homogeneous Poisson process). On the other hand, by considering that human errors do not depend on time, we used the exponential distribution for components and subsystems whose failure mode is human error (the Poisson process). This is an innovative contribution because it is based on the participation of the failures in different machining areas. The man-machine system proposed was designed based on the causal relationship between the failures occurring in different machining areas, where the components represent the sub-causes of failures and the subsystems represent the places where failures occur. The series-parallel configuration given to this system allowed us to find statistical models to evaluate the reliability of the component-subsystem relationship (Weibull and exponential distributions), of the subsystems (serial configuration), and of the man-machine system (parallel configuration). No man-machine systems were found to have been configured in a serial-parallel manner based on the participation of the failures. The Weibull and Exponential distributions were used due to the fact that, at the beginning of the research, it was assumed that the random variables involved in the failures within the man-machine system had a Weibull distribution and an exponential distribution. As the study developed, it was found that failures of mechanical and human-error origin were the most frequent occurrences in the machining area, proving these assumptions to be correct. The Weibull distribution is suitable for representing failures of mechanical origin because they are time-dependent, and the exponential distribution represents failures of human-error origin, which are not time-dependent. To monitor two sequential periods that have an exponential distribution in one of their component-subsystem relationships, it is only a matter of checking whether their reliability has improved or not and to act on the affected component. This is not the case with the Weibull distribution, where its parameters must be monitored to check whether the reliability has improved with the actions taken. Some proposed improvement actions, such as the use of the life-effort model, may help when the failure is caused by cutting tool wear. Because, in Weibull analysis, the shape parameter \(\beta\) characterizes the aging of the system, then in the Weibull reliability analysis the used \(\beta\) value plays a key role in accurately determining the reliability R(t) of the analyzed product. Moreover, because in practice \(\beta\) cannot be accurately estimated, then it is generally selected from historical data or from a baseline (a similar product). The estimation of the Weibull scale parameter \(\eta\) depends on both the estimated \(\beta\) value and on the desired R(t) index. The \(\eta\) parameter of the stress distribution is estimated by using R(t) = 0.9535 with n as an integer.