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This study is concerned with the problem of reliable dissipative control for a class of discrete-time switched singular systems with mixed time delays and multiple actuator failures. The failure probability of each actuator is individually quantified and is governed by an individual random variable satisfying a certain probabilistic distribution in the interval [0, 1]. Attention is focused on identifying a class of slow switching signals and designing a set of reliable mode-dependent state-feedback controllers such that, for all admissible mixed time delays and multiple probabilistic actuators faults, the closed-loop system is stochastically exponentially admissible and strictly (Q, Q, ℛ)-dissipative. By using the Lyapunov function approach and the average dwell-time scheme, sufficient conditions for the existence of such class of stabilising switching signals and the reliable mode-dependent controllers are derived in terms of linear matrix inequalities, and the explicit expression for the desired controller gains is also given. A numerical example is given to demonstrate the effectiveness of the theoretical results.