The particular power of remote vehicle emission sensing comes from the big sample size and the related statistical representativeness for emission rates derived. But how much data are needed for a representative measurement and when does the information gain per record become insignificant? Here we propose a systematic method in deciding sample size that saves monitoring cost without sacrificing statistical validity. We apply a bootstrap-sampling based Monte Carlo simulation approach to determine the relationship between sample size of emission measurement and statistical performance of sample mean estimators. We explore options in using a subset of the observed population to construct an empirical distribution that can be used to asymptotically infer statistics of the full population. We take the example of NO emissions from diesel cars measured between 2011 and 2018 at various locations in Europe. We find that as few as 100 and 250 instantaneous emission records of diesel cars approximate with 80% certainty the full population mean for EURO 4 or 5 and for EURO 6 exhaust emission standards, respectively, within 10% tolerance. We determine the relations for various tolerance margins and certainty requirements, so that experimentators can read off the numbers as needed. Further homogenization of the measurement conditions e.g. by temperature or driving condition can reduce this minimum sample size, as expected, but can also lead to more variability in exhaust emissions and hence require a larger minimum sample. This reflects how the exhaust emission controls have been tuned by manufacturers and cannot be estimated a priori. We expect much larger minimum sample sizes for other exhaust components. Hence, we here offer equations for a decent planning of a remote emission measurement campaign.

CICTP