The accurate due-date reliability evaluation of demand satisfaction is vital for due-time performance prediction of production systems. This paper proposes an improved multi-state reliability evaluation approach for production systems with finite buffers subject to time-dependent failures (TDFs), operation-dependent failures (ODFs). Instead of TDF machine model or ODF machine model, a modified machine reliability model considering both TDFs and ODFs is presented as a basis. And then an equivalent workstation reliability model is proposed by steady probability analysis of finite buffers. A united reliability calculating framework is constructed for the multi-state production system based on universal generating function. A case study of a piston production line is conducted to prove the feasibility and effectiveness of the proposed methodology.