Conformity-of-Production maximal number of tests: N=16 based on average and variation of test results average of all test results < limit - margin decreasing margin with the increasing number of tests start with N=3, stop at N=16 based on test variation with the number of tests the spread in the average decreases
Test each emission component against limit value COP Test each emission component against limit value Start with N=3 tests, determine average emission value X and standard deviation S, from the individual measurements xi: average: 𝑋= 1 𝑁 𝑖=1 𝑁 𝑥 𝑖 standard deviation: 𝑆= 1 𝑁−1 𝑖=1 𝑁 ( 𝑥 𝑖 −𝑋) 2 Pass if: 𝑋<𝑙𝑖𝑚𝑖𝑡 −𝑆 Fail if: 𝑋≥𝑙𝑖𝑚𝑖𝑡− 𝑁−3 13 ∗𝑆 Continue testing till decision (maximal N=16 tests) assuming normal probability distribution: pass at ~ 84% confidence incremental change: with N=3: X ≥ limit with N=16: X ≥ limit-S
average number of tests COP Simulations of the procedure with respect to limit = 1, homogeneous distributions average value min max pass rate average number of tests 0.980 0.95 1.01 88.8% 5.1 0.995 0.98 44.9% 5.7 1.005 0.99 1.02 4.0% 3.2 1.000 15.4% 4.1 0.950 0.80 1.10 43.2% 5.8 0.70 1.30 14.9% 1.20 29.4% 5.0 large spread: high fail rate limited test burden
The application of COP in type-approval testing Options: only Test Mass Low testing (limited burden) only Test Mass High testing both Test Mass High and Test Mass Low testing (completeness) Any vehicle production model in the CO2 family (mixed problem of testing and interpolation procedure)