Application of grey model GM(1, 1) to vehicle fatality risk estimation

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 US data sets yields exact predictions that are of high repeatability with characteristics depicting high reliability and efficiency. Another advantage is that these results are obtained without using any assumptions. In the analysis, the model normally deals directly with original data and searches the intrinsic regularity of data. The forecasting accuracy is related to the sample number n in grey model, and the accuracies for smoothed fatality risk predictions are higher than those for short-term predictions. The total time-dependent trends for these cases show very small variability between the real and prediction values, hence showing the theory to be working. For rollover cases, US data sets show that the risk of occupants to experience fatal injuries is decreasing and the fluctuating amplitude is declining. The theory predicted this trend and showed the time-dependent curves for data set and prediction to be in-phase. Another interesting observation that has come from the study is that UK and US experience similar phases in the time-dependent trend of motor vehicle fatality risk despite the different perception of safety between the USA and UK, especially when it comes to occupant usages of restraint systems.