On the estimation of temporal mileage rates

Mathematical and computational techniques are developed for the analysis of annual roadworthiness (MOT) test data that the UK Department for Transport has placed in the public domain. This paper develops a new theory to estimate fine-scale temporal (e.g., monthly) variations in vehicle mileage at a population level - derived from coarse-scale (e.g., annual) mileage data at an individual vehicle level. Numerical time-stepping schemes are derived from the theory and are tested on synthetic data to permit comparison with a known ground-truth mileage rate. Finally, we consider first steps in applying the methods directly to the MOT data set.