Division 4.3 Calculate the statistical error in the CO2 savings

The statistical error in the CO₂ savings is to be determined in two steps. In the first step the error value of the power is to be determined as a standard deviation being equivalent to a confidence interval of 68 %.

This is to be done by formula (4).

Formula (4) $S_{\bar{x}}=\sqrt{\frac{\sum _{i=1}^n{\left(x_i-\bar{x}\right)}^2}{n\left(n-1\right)}}$

Where:

$S_{\bar{x}}$

standard deviation of arithmetic mean [W];

x_i

measurement value [W];

$\bar{x}$

arithmetic mean [W];

n

number of measurements, which is 10.

Then the error in the CO₂ savings is to be determined using the propagation law, which is expressed in formula (5).

Formula (5) $\stackrel{–}{{\mathrm{\Delta C}}_{{\mathrm{CO}}_2}}=\sqrt{\sum _{i=1}^n{\left(\frac{{\mathrm{\partial C}}_{{\mathrm{CO}}_2}}{\mathrm{\partial P}}\times {\mathrm{eP}}_i\right)}^2}$

Where:

ΔC_CO2 :

mean total error of the CO₂ saving (gCO₂/km)

∂ C_CO2 /∂P

sensitivity of calculated CO₂ saving related to input value x_i

eP_i:

error of input value (W)

Substituting formula (2) in formula (5) leads for petrol fueled vehicles to:

Formula (6) ${\mathrm{\Delta C}}_{{\mathrm{CO}}_2}={\mathrm{0,0090\; gCO}}_2∕\mathrm{kmW}\times \mathrm{eP}$

Where:

ΔC_CO2

the error in the CO₂ savings (g CO₂/km);

eP

the error in the power consumption (W).

Substituting formula (2) in formula (5) leads for diesel fueled vehicles to:

Formula (7) ${\mathrm{\Delta C}}_{{\mathrm{CO}}_2}={\mathrm{0,0085\; gCO}}_2\mathrm{/kmW}\times \mathrm{eP}$

Where:

ΔC_CO2

the error in the CO₂ savings (g CO₂/km);

eP

error in the power consumption (W).