Abstract This article proposes a new random event‐triggering scheme to design filter of positive semi‐Markovian jump systems with intermittent sensor faults. To obtain a balance of saving network resources and improving system performance, a random event‐triggering mechanism consisting of time‐ and event‐triggering modes is constructed. A Bernoulli distribution‐based stochastic variable is introduced to orchestrate the switching of two triggering modes. A concept of hybrid gain performance is presented to guarantee that the filter can attenuate the affect from the disturbance and sensor faults. Then, a random event‐triggered filter is designed for positive semi‐Markovian jump systems subject to intermittent sensor faults. Under the designed filter, hybrid gain performance is achieved. Furthermore, the proposed approach is extended to the systems with stochastically incorrect sensor measurement. A linear programming method is employed for describing and computing the presented conditions. Finally, the validity of the results is verified via two examples.