Grey system theory can effectively deal with incomplete and uncertain information. However, there always exists a time lag just the same as other forecasting methods do although its application can yield exact prediction that are of high repeatability with characteristics depicting high reliability and efficiency. To minimise the lag time for the results of grey prediction, a 3-point moving average has been developed and applied on them.

A mathematical model known as Grey Model GM(1, 1) has been herewith employed successfully in the estimation of vehicle fatality risk. Its application to the UK and USA datasets has been proved to be greatly successful and reliable. The mean and maximum errors of the outcomes of grey prediction are tremendously reduced, hence greatly improving the accuracy of prediction. The forecasting accuracy is related to the sample number n in grey model. For rollover cases, USA datasets show that the risk of occupants in passenger cars to experience fatal injuries is decreasing and the fluctuating amplitude is declining too;​ but the time-dependent trend for the rollover fatality risk of light truck occupants is unclear and the fluctuating amplitude is in an unstable state. This shows that the rollover fatality risk hasn’t been controlled effectively at present and more research work needs to be done in the future for light trucks. Another interesting observation that has come from the study is that UK and USA experiences similar phases in the time-dependent trend of motor vehicle fatality risk despite the different perception of safety between USA and UK, especially when it comes to occupant usages of restraint systems.