Abstract: Finite Markov chain embedding approach is employed to compute the reliability function for complex systems, and the general formula of failure rate function is deduced from the relationship between reliability function and failure rate function.The computing process of complex systems' failure rate is then given.For a general complex system whose components are independent and distributed differently, the failure rate is given through the above approach.This approach can solve some problems that can not be solved by traditional approaches, and has its operability and validity.This study establishes a foundation to find out new characteristics of complex systems.