Multicarrier multipactor, which is found in the wideband high power vacuum microwave passive components, potentially threatens the reliability of microwave systems in space and accelerator applications. The global threshold analysis of multicarrier multipactor is of vital importance for the risk assessment of high power vacuum devices. Till now, however, no effective solutions for the global threshold analysis of multicarrier multipactor have been proposed for practical microwave components with complex structures. In this paper, an efficient approach capable of evaluating the global threshold of multicarrier multipactor based on detectable level of multipactor test system is presented. Electromagnetic characteristics of the microwave device are theoretically related to the electron density by equivalently considering the distribution zone of electrons as a plasma medium. In order to obtain the global threshold using the optimization algorithm, such as the Monte Carlo method, we further propose an efficient approach capable of rapidly computing the fluctuation of number of electrons in the evolving process of a multicarrier multipactor based on the equivalency of half-sine-like segments for the acceleration of electrons. Analytical results comply with the tested thresholds. Different from the conventional equivalent power using the empirical rule, the proposed approach is based on the criterion of critical density of electrons and rapidly computing the fluctuation of number of electrons, providing an efficient method for the accurate global threshold analysis of multicarrier multipactor.