COP statistic proposal for UN-WLTP Update February 2019

COP Status of ACEA proposels for COP procedure presented in December 2018 TNO definition for COP requirement & possible corresponding concept Proposal to generate test data

2 concepts for COP procedure proposed December 2018 Reminder: Proposal 1: Modified R83 approach Shortened to a max. sample size of 16 vehicles. Pass/fail threshold adjusted: Producer risk linked to actual ISC rules,if possible Keeping high uncertainty zone at begin of sampling Proposal 2: Testing by attributes Sample plan,same as defined for ISC Specific complementary element as substitute for outliers.

Proposal 1 Status: New set of pass/fail threshold numbers (=proposal 1.2) The standard deviation has no influence on the pass/fail probabilities. Chance to pass with 40% is 89.7%, i.e. ~10% producer risk Chance to pass with 65% is 14.6%, i.e. ~15% consumer risk

Proposal 1 Comparison with initial proposal from December 2018 Initial thresholds (Proposal 1) new thresholds (Proposal 1.2)

TNO definition With the confidence of 90% or higher it should be established that the (true) average CO2 emissions of a vehicle family (in CoP) is below the declared value. Based on this statement a further proposal (no. 3) has been developed.

confidence intervalls for average Proposal 3: confidence intervalls for average Two options Calculation of lower and upper confidence bounds based on predefined (accepted) standard deviation (z distribution);e.g. one number for CO2 and another number for regulated pollutants. Predefined standard deviation as part of the regulation can support the understanding that protection against variation is not overdeclaration. Calculation of lower and upper confidence bounds based on standard deviation from measurement data of the sample (t distribution). Bigger uncertainty of standard-deviation compared to 1. leads to wider continue zone.

confidence intervalls for average Proposal 3: confidence intervalls for average Option 1 and 2 ,as well as current WLTP pass/fail thresholds are shown in the graph. It is obvious that current regulation is in conflict with the expectation to assess with 90% confidence that the average is below limit/declared value. To be 90% confident that the true average of the population does not exceed the declared value,the average of the sample needs to be below 96,2

Comparison of concepts The following slides show the probability for pass,fail and continue conditions as function of the sample size for Regulation 1151 and ECE R83 Proposal 1.2 (latest thresholds) and for Proposal 3,Option 2 :one sided confidence interval,σ calculated from measurements in the sample The graphs are shown for a defective rate of 40% and a standard deviation of 2% of the “limit” (i.e. realistic CO2 variation)

Probability comparisons for statistics of regulation

Probability comparisons for statistics of selected alternatives Proposal 3,option 2 Proposal 1.2,new thresholds

Selection criteria (1/2) 1151 A=1,05 R83 Proposal 1.2 Proposal 3,option 2 Fast decision + - o High pass probability Low fail probability Producer risk* for 40% defective (max. sample size) 12 % 5% 10 % 32 % Consumer risk* for 65% defective (max. sample size) 52 % 10% 15 % 20 % ACEA preference X * Assumed standard deviation of population:10% High pass & high fail probability (1151) vs. Low fail probability and higher test burden (R83,Proposal1.2). Proposal 3,opt. 2 provides a slight advantage in lower fail probability compared to 1151 with the cost of a continue area close to R83.

Selection criteria (2/2) 1151 A=1,01 R83 Proposal 1.2 Proposal 3,option 2 Fast decision + - o High pass probability Low fail probability Producer risk* for 40% defective (max. sample size) 10 % 5% 19 % Consumer risk* for 65% defective (max. sample size) 58 % 10% 15 % 8 % ACEA preference X * Assumed standard deviation of population:2 % High pass & high fail probability (1151) vs. Low fail probability and higher test burden (R83,Proposal1.2). Proposal 3,opt. 2 provides a slight advantage in lower fail probability compared to 1151 with the cost of a continue area close to R83.

Generation of test data Realistic data are needed to test/validate the COP procedure options. Proposal is to generate random data for given (confirmed) average m and standard deviation s.

Conclusion ACEA is voting for a new COP statistical procedure based on proposal 1.2 or proposal 3 (option 2) – to be further optimized. Optimizing COP sampling frequency,considering Japan procedure To confirm grouping criteria for sampling process.

Back up

Selection criteria (2/2) 1151 A=1,01 R83 Proposal 1.2 Proposal 3,option 2 Fast decision + - o High pass probability Low fail probability Producer risk* for 40% defective (max. sample size) 15 % 5% 10 % 22 % Consumer risk* for 65% defective (max. sample size) 50 % 10% 12 % * Assumed standard deviation of population:3 % High pass & high fail probability (1151) vs. Low fail probability and higher test burden (R83,Proposal1.2). Proposal 3,opt. 2 provides a slight advantage in lower fail probability compared to 1151 with the cost of a continue area close to R83.

Passing probability plots (max. sample size)

Passing probability plots (max. sample size) Proposal 1.2 (modified R83) The standard deviation has no influence on the pass/fail probabilities.

Passing probability plots (max. sample size) Proposal 3,Option 2