To analyze the effect of performance dependence caused by interaction among units on the reliability of multi-state system, the function-motion-action (FMA) theory is used to decompose a multi-state system into meta-actions. By using the non-homogeneous Markov model, the multi-state evolution process of the meta-action unit is described. By setting the state transition coefficient to associate the state transition rate with the dependency property, a new state transition matrix is constructed. The Kolmogorov differential equation is used to obtain the probability. The model considering the performance-dependent characteristics of the units is established by the vector universal generation function. The index turntable system is used as an example to verify the influence of the unit dependence characteristics on the system. The results show that the state transfer rate will change with the performance degradation of the free cells. Compared with the multi-state system with independent units, when the unit is in a high performance state, the multi-state system with unit-dependent characteristics is more reliable. On the contrary, the system is more vulnerable. The results provide theoretical basis for the reliability design and the product maintenance cycle setting.