When is Enough? Minimum Sample Sizes for On-Road Measurements of Car Emissions

The power of remote vehicle emission sensing stems from the big sample size obtained and its related statistical representativeness for the measured emission rates. But how many records are needed for a representative measurement and when does the information gain per record become insignificant? We use Monte Carlo simulations to determine the relationship between the sample size and the accuracy of the sample mean and variance. We take the example of NO emissions from diesel cars measured by remote emission monitors between 2011 and 2018 at various locations in Europe. We find that no more than 200 remote sensing records are sufficient to approximate the mean emission rate for Euro 4, 5, and 6a/b diesel cars with 80% certainty within a +/- 1 g NO per kg fuel tolerance margin (similar to +/- 50 mg NO per km). Between 300 and 800 remote sensing records are needed to approximate also the variance of the mean NO emission rates for those diesel car technologies. This translates to only 2 and up to 9 measurement days to characterize the means and their variance for a car fleet typical in Europe.