Division 4.3 Calculation of the statistical error in the CO2 savings

United Kingdom

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 % around the mean.

This is to be done by formula (5).

Formula (5):

s_{\bar{x}} = \sqrt{\frac{\sum_{i = 1}^{n} {(x_{i} - \bar{x})}^{2}}{n (n - 1)}}

Where:

s_{\bar{x}}

Standard deviation of the sample mean [W]

x_i

Sample data [W]

\bar{x}

Mean of the sample data [W]

Number of observations of the sample, which is five.

In order to calculate the error in the CO₂ savings for petrol, petrol turbo and diesel-fuelled vehicles, the propagation law, expressed in formula (6), is to be applied.

Formula (6):

s_{C_{{CO}_{2}}} = \sqrt{\sum_{j = 1}^{m} {(\frac{{θC}_{{CO}_{2}}}{{θP}_{j}}_{P_{j} = {\bar{P}}_{j}} \times s_{{\bar{P}}_{j}})}^{2}}

Where:

s_{C_{{CO}_{2}}}

Standard deviation of the total CO₂ saving [gCO₂/km]

\frac{{θC}_{{CO}_{2}}}{{θP}_{j}}_{P_{j} = {\bar{P}}_{j}}

Sensitivity of calculated CO₂ saving related to P_j

s_{{\bar{P}}_{j}}

Standard deviation of ${\bar{P}}_{j}$ [W]

Number of types of lighting in the innovative technology package

Substituting formula (2) in formula (6) results in formula (7) for calculating the error in CO₂ savings for petrol-fuelled vehicles.

Formula (7)

s_{C_{{CO}_{2}}} = {0,0273 gCO}_{2} ∕ kmW \times \sqrt{\sum_{j = 1}^{m} {({UF}_{j} \times s_{{\bar{P}}_{j}})}^{2}}

Substituting formula (3) in formula (6) results in formula (8) for calculating the error in CO₂ savings for diesel-fuelled vehicles.

Formula(8):

s_{C_{{CO}_{2}}} = {0,0258 gCO}_{2} ∕ kmW \times \sqrt{\sum_{j = 1}^{m} {({UF}_{j} \times s_{{\bar{P}}_{j}})}^{2}}

Substituting formula (4) in formula (6) results in formula (9) for calculating the error in CO₂ savings for petrol-fuelled vehicles with turbo charger.

Formula (9):

s_{C_{{CO}_{2}}} = {0,0290 gCO}_{2} ∕ kmW \times \sqrt{\sum_{j = 1}^{m} {({UF}_{j} \times s_{{\bar{P}}_{j}})}^{2}}