In this paper, a new operator splitting method is proposed for capturing stiff and nonstiff detonation waves. In stiff cases, an incorrect propagation of discontinuities might be observed for general shock-capturing methods due to under-resolution in space and time. Previous random projection methods have been applied successfully for stiff detonation capturing at under-resolved conditions. Not relying on random projection of the intermediate state onto two presumed equilibrium states (completely burnt or unburnt) as with the random projection method, the present approach randomly advances or interrupts the reaction process. Each one-way reaction is decoupled from the multi-reaction kinetics by operator splitting. The local temperature is compared with a random temperature within a temperature interval to control the random reaction. Random activation or deactivation in the reaction step serves to reduce the accumulated error of discontinuity propagation. Extensive numerical experiments demonstrate the effectiveness and robustness of the method. For nonstiff problems, the proposed random method recovers the accuracy of general operator splitting methods by adding a drift term. (C) 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.