On the estimation of temporal mileage rates

Mathematical and computational techniques are developed for the analysis of annual MOT (roadworthiness) test data that the UK Department for Transport has placed in the public domain. This paper focusses on the development of a new theory which has the potential to estimate fine-scale temporal variations (e.g., monthly) in vehicle mileage at a population level, that we call the spot rate — derived from coarse-scale (e.g., annual) mileage data at an individual vehicle level. Due to the availability of data, the focus is on the UK situation, but the theory has applications to any data set internationally, where odometer readings of individual vehicles are monitored on an occasional basis. 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. It is found that for practical applicability, the methods need to pre-process data with smoothing filters (a full investigation of which is beyond the scope of this paper). Finally, we consider first steps in applying the methods directly to the MOT data set and the remaining problems that must be solved for them to become a practical reality.