# The Relationship between Process Capability and Quality of Measurement System
## 1 Introduction
C\({}_{\rm PL}\) or P\({}_{\rm PL}\) are measures of the potential capability of the process based on its lower specification limit. They are ratios that compare two values: the distance from the process mean to the lower specification limit (LSL) and the one-sided spread of the process (the 3-\(\sigma\) variation) based on the within-subgroup standard deviation. C\({}_{\rm PU}\) or P\({}_{\rm PU}\) are measures of the potential capability of a process based on its upper specification limit. C\({}_{\rm PU}\) is a ratio that compares two values: the distance from the process mean to the upper specification limit (USL) and one-sided spread of the process (the 3-\(\sigma\) variation) based on the variation within the subgroups. Because it considers both the process mean and the process spread, it evaluates both the location and variation (within subgroups) of the process [3]. After evaluating the data measured by metrological appraiser A, it was found that all 45 shafts met the USL tolerance requirement. On the other hand, up to 57.78% of shafts had a diameter smaller than LSL. As can be seen from Table 1, as a result, the C\({}_{\rm P}\) capability index was very low (0.8834), as was the C\({}_{\rm PK}\) index, which signaled a process deviation. This was also confirmed by the average value of the observed dimension (7.9588). It exceeded the LSL value by only 0.0003 mm. This would represent a failure rate of 550,000 ppm. The same shafts have already been produced in the past. The nonconformities also occurred at that time, but not to such an extent. Customers complained about increased noise and disturbing sound effects. According to regulations [4; 5], the upper permissible noise level of the drill is 90 dB. A noise level of 93.3 dB was measured for the drills complained about by the customer. The measurement was tentative, as an uncertified measuring instrument was used. In addition to the excessive noise, an unpleasant, disturbing noise also occurred. The cause of these disturbing sound effects may have been the excessive clearance between the shaft and the bearing, allowing the shaft to vibrate. Due to the large number of nonconforming products, production was stopped. It was necessary to analyze the causes of nonconforming product occurrence. Based on the analysis, effective corrective action had to be taken. A cause-and-effect diagram was used in the analysis to determine the causes and consequences (Figure 1). This diagram has been used by several authors, such as [PERSON] et al. [6; 7; 8; 9; 10], as the basis of fault analysis. It allows for a \"clarification\" of the problem and is often used to identify the sources that contribute to the analyzed problem and the relationships between them [11; 12; 13; 14]. As can be seen in Figure 1, the consequence--problem statement--is a high number of nonconforming (defective) shafts (high ppm of defective shafts). The categories were modified according to actual problems in the process of shaft production (Manpower, Materials, Methods, Measurement, Environment and Machine). The category \"Manpower\" is extremely important because the factors involved also influence other categories. It mainly represents the appraiser of the CNC lathe (metrological appraiser is included in the Measurement category). Possible sub-causes are incompetence, setting error, inappropriate interventions into the CNC machine during production, no input and output control and noncompliance with regulations. Two possible causes have been identified in the category \"Materials\": inappropriate material or material swap (mismatch), either in terms of its composition or dimensions. This may be due to poor records or a poor measurement system. Two possible causes were also identified in the category \"Methods\": incorrect method of metrological traceability maintenance and incorrect use of the metrological procedure of the organization. It should be noted that the metrological order is confusing, difficult to understand and can lead to errors.