# Metrics Related to Confusion Matrix as Tools for Conformity Assessment Decisions
## 2 Materials and Methods  
### Production Process and Improvement Procedure  
In this paper, the effect of measurement uncertainty on conformity assessment has been analyzed based on the measurement of the inner diameter of a bearing ring. By monitoring the production process and quality control process in one Croatian company, it was established that there is a significant percentage of non-conforming units. The existing quality control was conducted by workers after each production phase using manual gauges and devices for controlling measurements (Figure 3). Specific dimensions and geometric characteristics of the bearing ring were 100% controlled, while the others were sampled for control by randomly choosing 3 to 10 products. Such a control system did not always ensure the delivery of conforming products. Because of this, the existing product quality control process had to be changed. Changes have involved the implementation of the new automated measurement system (Figure 4). The new measurement system enabled the conducting of measurements of specified dimensions and geometric characteristics in 100% of cases, as well as monitoring production process capabilities and measurement system quality. In addition, the new automated system can continuously monitor and store results and sort products (separating bad products  
Figure 3: Initial measurement system. from good products). Although the purpose of quality control is not sorting products, but rather obtaining and maintaining control over the process and continuous improvement of the process; the goal of sorting the products is to minimize the possibility of customers receiving a non-conforming product. An automated measurement system removes the human factor from the measurement process, which significantly reduces the measurement uncertainty of measurement results. Continuous monitoring and analysing measurement results enables for timely response during the production process and, thus, prevents the manufacturing of non-conforming products. When the measurement system detects a non-conforming product, that particular product will not be delivered to the customer. However, regardless of the quality of a measurement system, the measurement system will always comprise measurement uncertainty, which can lead to making wrong decisions. To this end, this paper analyses the effect of measurement uncertainty on global producer's and consumer's risk, which is why the optimal acceptance interval limit has to be determined. This paper analyses risk based on the measurement of the inner diameter of a bearing ring, with a nominal value of 100 mm. According to the producer's specifications, tolerance field for inner diameter equals \(\pm\) 0.022 mm. The effect of measurement uncertainty on non-conformity assessment was observed for the inner diameter of the bearing ring because that dimension was 100% controlled using the initial (previous) and improved (new) measurement system. Following experimental results of two measurement systems (initial and improved) were used as input data for the mathematical model. The nominal value of the inner diameter of the ring of the initial model is \(\overline{y}=100.008\) mm with standard deviation of \(u_{0}=0.011\) mm. The subsequent inspection process was carried out with a measurement uncertainty of \(u_{m}=0.005\) mm. With the improved production process for the nominal value of the inner diameter of the ring, it was obtained by measurement that \(\overline{y}=100.004\) mm with standard deviation of \(u_{0}=0.0066\) mm. The measurement uncertainty of the control quality process associated with the improved model amounts to \(u_{m}=0.0015\) mm. In the further text, the terms improved model, improved process, and improved measurement system are identified. The same applies for the term initial model. Figure 4: New automated measurement system. Different stages of the automated measurement process.