Abstract: In this paper, we consider a repairable M/M/(1+c) queueing system with two-phase service and redundant dependencies, in which the second service is provided by c identical servers who randomly provide two types of services to the customers. The customers who enter the system are divided into type 1 customers and type 2 customers. If the waiting room of the second phase is not fully occupied, the type 2 customers can directly enter the second phase. In practice, there are various dependencies among the failure behaviors of the servers, which are called failure dependencies. We present a redundancy function to determine the failure rate of servers. We first derive the steady-state probabilities and performance measures of the system by quasi-birth-and-death (QBD) process theory and Matrix-geometric solution method. Next, we provide numerical examples to illustrate the effects of four types of redundant dependence on performance measures. Then, we construct a bi-objective optimal model and provide a scoring method that makes it possible to achieve an appropriate balance between the system cost and the service quality. Finally, the regression equation between the minimum cost and the waiting time is proposed, which is helpful to determine the minimum cost that meets service quality.