# Metrics Related to Confusion Matrix as Tools for Conformity Assessment Decisions
## 3 Results and Discussion  
### Risk Analysis  
Specific producer's and consumer's risks, as well as global producer's and consumer's risks, have been calculated for both the initial and improved models. According to Formula(1), the conformance probability is calculated using a single integral and does not depend on the length of the guard band.  
Therefore, the values for the specific producer's risk \({R_{P}}^{*}=p_{C}\), and the specific consumer's risk \({R_{C}}^{*}=1-p_{C}\), are identical to each of the models described in Figure 2, regardless of the length of the guard band. The values of the specific producer's and consumer's risk are higher with the improved model. With the initial model, the value of the specific producer's risk is \({R_{P}}^{*}=89.52\%\), and the specific consumer's risk is \({R_{C}}^{*}=10.48\%\). With the improved model, \(99.67\%\) of the rings meet the specifications, and the measured value of the inner diameter of these rings is within the given tolerance interval. Only 0.33% of rings are not conformed to the specification.  
The global producer's and consumer's risks of the improved model are lower compared to the initial model (Figure 6).  
The values in Figure 6, as well as on all subsequent figures, should be viewed in two directions, regarding the sign of the length of the guard band. Negative values for a guard band in Figure 6 are respective to the model of the minimization of the producer's risk and refer to the case described in Figure 2a, when the tolerance interval is within the acceptance interval. A smaller negative value represents a wider guard band. If the value of the guard band is equal to zero, the tolerance interval is equal to the acceptance interval, as shown in Figure 2b. Positive values of the guard band correspond to the model of minimization of the global consumer's risk (Figure 2c). A larger positive value indicates a larger length of the guard band \(w\).  
Unlike the specific risk, the global risks have different values for the different lengths of the guard band. The global producer's risk is the lowest in the case when the length of the guard band is \(\mathrm{w}=-0.0025\) mm, and the highest if it is \(\mathrm{w}=0.0025\) mm (Figure 6a). For the global consumer's risk, the opposite is true (Figure 6b).  
Values for global consumer and producer risk are usually expressed as percentages. Multiplying these probabilities by 10,000 results in the number of falsely accepted and falsely rejected rings per piece. This multiplication has been conducted for simplicity. These values also can be multiplied by 100, 1000, or any other number that represents the daily, weekly, monthly, or yearly production of bearing rings or some other product. The number of falsely accepted and falsely rejected rings is lower in the improved model than in the initial one. The reduction of scrap and, thus, the decrease in production costs for  
Figure 6: Initial versus improved model: (**a**) Global producer’s risk; (**b**) Global consumer’s risk.  
the manufacturer and the reduction of the risk of purchasing rings that do not conform to specifications are shown in Table 1. The number of rings that were falsely accepted or falsely rejected is given per piece. The values are shown for the characteristic lengths of the guard band.