3rd ICAI 2024

International Conference on Automotive Industry 2024

Mladá Boleslav, Czech Republic

How to interpret the data in the table. Let’s assume that as a result of (correct) calculations, we have obtained the value of the indicator Ĉ p = 2 (the last row of Table 1). Let’s also assume that a total of 100 items (sample size n = 100) were collected for the purposes of the calculations. At the intersection of the row and column, we get the value of, which should be interpreted as the lower bound of the confidence interval with a confidence level of 0,99. To sum up, with the calculated index Cp = 1,663 Ĉ p = 2 for n = 100, in reality (99%) there should be no lower value of the Cp index than 1,663. When designing the measurement system and selecting the measuring device with the required resolution, it is proposed to adopt the lower values of the Cp indicator presented in Table 1 and the modified formula (4) presented below: On the basis of formula (5) and the assumption that we want to measure samples (n = 100) with sufficient resolution so as to be able to show the value of the Cp index at the level of 1,66 (1,663), we should select the resolution of the instrument according to the Tol/ 10 * 2 = Tol/20 principle, because Ĉ p = 2 for the assumed value at n = 100 – see Table 1. The higher the resolution of the instrument, the smaller its scale division. Dividing the tolerance range by 20 to determine the resolution of the instrument has also been proposed in the book [5]. Sometimes this requirement is difficult to meet. If we plan to collect a different number of samples (e.g. n = 120) on the basis of which the value of the Cp index will be calculated, or if we want to use a less restrictive confidence interval, e.g. 0, 95, or when we are interested in a different target value of the Cp index, different data should be used on the basis of the appropriate tables [2]. 2.2 Examples for analog and digital instruments Using analog measuring instruments, we are most often dealing with meters made in a certain class of accuracy. Knowing the accuracy class of the measuring instrument, we are able to determine the value of the maximum uncertainty characterizing the results of the measurements obtained by the instrument. For example, an analogue voltmeter with accuracy class 1 and a measuring range of e.g. 30 V will be characterized by maximum uncertainty resulting from its construction For a digital voltmeter, the formula for determining the maximum uncertainty is slightly different. For example, Accuracy is defined by formula 0,5% + 2D. This means that if we received a result of e.g. 24.00 V on the display, we can assume that ∆U = 0,5% * 24,00V + 2 * 0,01 = 0,14V. Let’s assume that the tested voltage is covered with a range of permissible changes of +/- 1V, i.e. T = 2V. The question is whether the digital meter presented above will provide the results of the measurements allowing to conduct statistical analyses at the level of Cp = 2. The resolution r should be treated as a number, i.e. the smaller the better. An instrument with a resolution of 0,01, e.g. a digital caliper, will be better than another instrument with r = 0,05 – an analogue caliper.

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