3rd ICAI 2024

International Conference on Automotive Industry 2024

Mladá Boleslav, Czech Republic

Let’s assume that we use the rule of 1 to 10 for the variability of the process, which at the value of the Cp index > 1 will be less than the tolerance area. Using the above mentioned rule, it can be written that the required resolution of the instrument r should be:

After substitution, we get:

Analysing the above formula, we can see that if we were to apply the rule of 1 to 10 directly in relation to tolerance to determine the required resolution of a measuring instrument (and this is often done in industrial practice), it would be correct for the value of Cp = 1. Very often, the required value of the Cp is 1,33 or 1,67 or higher. In addition, it should be remembered that the values of the process capability index calculated on the basis of measurements are random variables, so their values estimated as a result of statistical research are estimators of these indicators. Since in practice it is very difficult to find estimators that are consistent, unbiased and the most effective, it is necessary to determine a confidence interval for the estimated value of the indicator. We will be mainly interested in the lower values of the confidence interval. Examples of lower end values for the Cp at the confidence level of 0,99 are presented in Table 1 [8].

Table 1: The lower limit of the confidence interval for the Cp indicator is determined at the confidence level of 0.99

Source [7, 8]

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