Document ID: chunk:federal_register_of_legislation:F2023C00229:reg:5:p35
Version: federal_register_of_legislation:F2023C00229
Segment Type: reg
Provision Reference: reg 5 (pt 35/36)
Character Range: 518045–520672

by the following:

'3. The following procedure is used for each of the pollutants given in section 6.2.1 of Annex I (see Figure 2):

Let:

L = the natural logarithm of the limit value for the pollutant
xi = the natural logarithm of the measurement (after having applied the relevant DF) for the i-th engine of the sample
s = an estimate of the production standard deviation (after taking the natural logarithm of the measurements)
n = the current sample number.'

     (u)    In Appendix 2, section 3 and the introductory phrase of section 4 are replaced by the following:

    '3. The values of the pollutants given in section 6.2.1 of Annex I, after having applied the relevant DF, are considered to be log normally dis- tributed and should be transformed by taking their natural logarithms. Let m0 and m denote the minimum and maximum sample size respec- tively (m0 = 3 and m = 32) and let n denote the current sample number.

    4. If the natural logarithms of the measured values (after having applied the relevant DF) in the series are x1, x2,… xi and L is the natural loga- rithm of the limit value for the pollutant, then, define:'

     (v)     In Appendix 3, section 3 is replaced by the following:
    '3. The following procedure is used for each of the pollutants given in section 6.2.1 of Annex I (see Figure 2): Let:

L = the natural logarithm of the limit value for the pollutant
xi = the natural logarithm of the measurement (after having applied the relevant DF) for the i-th engine of the sample
s = an estimate of the production standard deviation (after taking the natural logarithm of the measurements)
n = the current sample number.'

     (w)   A following Appendix 4 is added:

'Appendix 4

DETERMINATION OF SYSTEM EQUIVALENCE

    The determination of system equivalency according to section 6.2 of this Annex shall be based on a 7 sample pair (or larger) correlation study between the candidate system and one of the accepted reference systems of this Directive using the appropriate test cycle(s). The equivalency criteria to be applied shall be the F-test and the two-sided Student t-test.

    This statistical method examines the hypothesis that the population standard deviation and mean value for an emission measured with the can- didate system do not differ from the standard deviation and population mean value for that emission measured with the reference system. The hypothesis shall be tested on the basis of a 5 % significance level of the F and t values. The critical F and t values for 7 to 10 sample pairs are given in the table below. If the F and t values calculated according to