where Tf is the available lifetime of the vehicular fuel cell, P isthe limited rate of performance decay at the end of lifetime, kpis an accelerating coefficient related to factors such as gas qualitydifference, P1’, P2’, P3’, and P4’ are the decay rates corresponding to load changing, startup-shutdown, idling, and the high power conditions, respectively, n1 and n2 are the related cycle times, and t3 and t4 are the operating time under specific conditions.