Document ID: chunk:federal_register_of_legislation:F2023C00229:reg:4:p41
Version: federal_register_of_legislation:F2023C00229
Segment Type: reg
Provision Reference: reg 4 (pt 41/42)
Character Range: 120123–125139

sampling procedure is set so that the probability of a lot passing a test with 40 % of the engines defective is 0,95 (producer's risk = 5 %) while the probability of a lot being accepted with 65 % of the engines defective is 0,10 (consumer's risk = 10 %).

         3.      The values of the pollutants given in Section 6.2.1 of Annex I are considered to be log normally distributed and should be transformed by taking their natural logarithms. Let m0 and m denote the minimum and maximum sample size respectively (m0 = 3 and m = 32) and let n denote the current sample number.

         4.      If the natural logarithms of the values measured in the series are χ1, χ2, … χi and L is the natural logarithm of the limit value for the pollutant, then, define

 and

         5.      Table 4 shows values of the pass (An) and fail (Bn) decision numbers against current sample number. The test statistic result is the ratio: dn=Vn and shall be used to determine whether the series has passed or failed as follows:

         for m0 ≤ n < m:

           —    pass the series if dn=vn ≤ An,
           —    fail the series if dn = vn≥ Bn,

           —    take another measurement if An< dn=vn < Bn.

         6.      Remarks

         The following recursive formulae are useful for calculating successive values of the test statistic:

        Table 4

                    Pass and fail decision numbers of Appendix 2 sampling plan Minimum sample size: 3
      Cumulative number of engines tested (sample size)
                                                            Pass decision number An      Fail decision number Bn
 3                                                          − 0,80381                    16,64743
 4                                                          − 0,76339                    7,68627
 5                                                          − 0,72982                    4,67136
 6                                                          − 0,69962                    3,25573
 7                                                          − 0,67129                    2,45431
 8                                                          − 0,64406                    1,94369
 9                                                          − 0,61750                    1,59105
    10                                                      − 0,59135                    1,33295
    11                                                      − 0,56542                    1,13566
    12                                                      − 0,53960                    0,97970
    13                                                      − 0,51379                    0,85307
    14                                                      − 0,48791                    0,74801
    15                                                      − 0,46191                    0,65928
    16                                                      − 0,43573                    0,58321
    17                                                      − 0,40933                    0,51718
    18                                                      − 0,38266                    0,45922
    19                                                      − 0,35570                    0,40788
    20                                                      − 0,32840                    0,36203
    21                                                      − 0,30072                    0,32078
    22                                                      − 0,27263                    0,28343
    23                                                      − 0,24410                    0,24943
    24                                                      − 0,21509                    0,21831
    25                                                      − 0,18557                    0,18970
    26                                                      − 0,15550                    0,16328
    27                                                      − 0,12483                    0,13880
    28                                                      − 0,09354                    0,11603
    29                                                      − 0,06159                    0,09480
    30                                                      − 0,02892                    0,07493
    31                                                      − 0,00449                    0,05629
    32                                                      − 0,03876                    0,03876

        Appendix 3

       PROCEDURE FOR PRODUCTION CONFORMITY TESTING AT MANUFACTURER'S REQUEST

           1. This Appendix describes the procedure to be used to verify, at the manufacturer's request, production conformity for the emissions of pollutants.

         2.      With a minimum sample size of three engines the sampling procedure is set so that the probability of a lot passing a     test with 30 % of the engines defective is 0,90 (producer's risk = 10 %) while