On algorithms for effective speed-up simulation of reliability models

Alexandra Borodina, Vitaliy Tishenko
We consider a regenerative degradation process composed by a sum of the successive phases, where preventative maintenance is used to prevent instantaneous failure. Calculation of the failure probability and other characteristics of the regeneration cycle is critical for the optimal control of such systems. When an instantaneous failure is a rare event, this model is a good reference for testing the variance reduction techniques that were proposed earlier and speed-up simulation algorithms. In more general cases, when we need to use simulation we propose two scenarios of the splitting method to evaluate the characteristics of the degradation process more effectively than naive Monte Carlo.