# Metrics Related to Confusion Matrix as Tools for Conformity Assessment Decisions
## 3 Results and Discussion
### Guard Banding by Confusion Matrix  
The initial lengths of the guard band are the same for the initial and improved models, but they differ in sign depending on whether it was about minimizing the global risk of the producer or consumer. In this way, it is easier to compare the initial and improved model because the comparison is made in the same nodes of the subdivision of the interval \([-1,\ 1]\) for the same multiplicative factor \(r\). The highest value of the guard band for the model of minimization of the consumer's risk, shown in Figure 2c, is set to \(w=0.0025\) mm. In the model of minimization of the producer's risk, this value has a negative sign (Figure 2a). The initial length of the guard band can be larger or smaller than the specified one. In that case, the graphs for the global risk of producers and consumers, and for the selected metrics, will be displayed in a wider or narrower range, respectively. The corresponding values of the calculated risks and metrics will not change if the range of the graphs on the guard band axis is wider. The graphs will only have new values added for the extension points. It can be problematic if a small initial length of the guard band is set. Then, it can occur that characteristic points, such as the intersection of precision, recall, and F1 metrics, are not included in the displayed graph. If it is assumed that such characteristic points exist, it is necessary to increase the initial length of the guard band. The general question is, what is the optimal length of the guard band? Over the last few decades, many methods and recommendations for guard banding have been developed. In many applications, the length \(w\) of the guard band is assumed to be equal to the expanded uncertainty \(U\)[41; 42]. This means that \(w=2u_{0}=U\). Based on expanded uncertainty, guard band length can be established so that \(w=3U=6u_{0}\) (6 sigma rule) or \(w=1.5U=3u_{0}\) (3 sigma rule), [4]. A more complicated formula in which the length of the guard band is expressed through an exponential function is detailed in [43]. The length of the guard band can also be calculated using the test of uncertain ratio (TUR) [44; 45]. In addition, methods were developed where the acceptance interval was set by means of maximization of the revenue from processes without the systematic effect of measurement uncertainty [46] or with unknown systematic effect, [47]. Recently, methods have been developed to determine the guard band in multivariate models for total risk calculation [48; 49]. Furthermore, there is always the opportunity for producers and consumers to compromise and agree on the level of the risks. In that case, it is up to the producer to find the length of the guard for a given consumer risk. In this paper, the metrics associated with the confusion matrices were used to determine the optimal length \(w\) of the guard band. One option is to set the length of the guard band to suit the situation when \(R_{P}=R_{C}\). Another option is to take advantage of changes in the behaviour of the [PERSON]'s kappa and [PERSON]'s correlation coefficient metrics. For all the basic tested metrics, the values of the metric for the improved model are higher in comparison to the values of the metrics in the initial model. The only tested metrics that behave differently are kappa and [PERSON]'s correlation coefficient. There are change points for these two metrics. At these points, the curves of the improved model intersect the curves of the initial model (Figure 9). At the intersection points, the values of the kappa, or MCC metrics, are the same for the initial and improved models. The change point exists both in the producer's risk minimization model and in the consumer's risk minimization model. For \(w\in\epsilon\left[-0.0025,\ -0.001548\right]\) and \(w\in\left\langle 0.001003,\ 0.0025\right\rangle,\) the kappa statistics of the improved model \(kappa_{Im}\) are smaller than the kappa statistics of the initial model \(kappa_{Im}\).