Division 5 Standard deviation of the arithmetic mean value of the efficiency of the alternator

Statistical errors in the outcomes of the testing methodology caused by the measurements are to be quantified. The format of the error value is to be a standard deviation being equivalent to a two-sided confidence interval of 84 % (see formula (3)).

Formula (3)

$$s_{\bar{x}}=\sqrt{\frac{\sum _{i=1}^n{\left(x_i-\bar{x}\right)}^2}{n\left(n-1\right)}}$$

Where:

$s_{\bar{x}}$

standard deviation of arithmetic mean;

x_i

measurement value;

$\bar{x}$

arithmetic mean;

n

number of measurements

All measurements are to be performed consecutively at least five (5) times. For each speed the standard deviation is calculated.

The standard deviation of the efficiency value of the alternator (ΔηΑ) is calculated by the following formula:

Formula (4)

$${\mathrm{\Delta \eta }}_{{\rm A}}=\sqrt{\left(\mathrm{0,25\; *}{\left(S_{1800}\right)}^2+\mathrm{0,40\; *}{\left(S_{3000}\right)}^2+\mathrm{0,25\; *}{\left(S_{6000}\right)}^2+\mathrm{0,1\; *}{\left(S_{10000}\right)}^2\right)}$$

Where the values 0,25, 0,40, 0,25, and 0,1 are the same weighting values as in formula (2) and S_{1 800}, S_{3 000}, S_{6 000}, and S_{10 000} are the standard deviations calculated with formula (3).