A model for evaluating the effectiveness of motor vehicle inspection programs

A statistical model for the evaluation of the effectiveness of motor vehicle inspection programs in reducing highway crashes is presented. The model is based on the assumption that the waiting time between highway crashes follows an exponential distribution. Since highway crashes are relatively rare events, it is assumed that the length of the study period is such that censoring occurs. Under these assumptions, maximum likelihood estimates of the mean waiting time θ until a crash for the non-inspected (inspected) vehicles is obtained and the corresponding test statistic is derived. As mechanically-caused accidents are but a small part of the overall accident picture and since inspection should only affect this portion, sample size requirements are investigated for various combinations of θ, Δ (increase in average time until a crash due to the effect of inspection), L (length of study period), and = β (probability of Type I error equalling probability of Type II error). For reasonable Δ, the sample required is indeed sizable.