Worst-Case Software Safety Level for Braking Distance Algorithm of a Train

This paper presents a worst-case software safety level analysis of braking distance algorithm of a train. This analysis will prove that the safety critical software algorithm is valid. Sometimes algorithms cannot be shown to be valid through testing due to being too complex. The proposed approach should show the algorithm never goes outside a stated bound in worst case condition. The inputs are chosen to not only show the normal condition, but also include combinations of inputs at the worst case limits in order to show worst case performance of the algorithm. For braking distance algorithm the performance could vary depending on multiple varying inputs, such as the location, direction, speed or acceleration rate of a train. Only algorithm related errors are considered in the present analysis. Hardware related errors are not considered in this analysis. The analysis is done for different algorithms such as single order interpolation and 2^nd order interpolation equations. The analysis result shows that single order interpolation algorithm gives better results than 2^nd order interpolation algorithm. In the analysis report the safety level is shown for different train speeds for high speed passenger train and freight train. The analysis is carried out for rounding error, division-by-zero, overflow error and underflow error.