Abstract: The state transition chain method is discussed and demonstrated as a method of reliability analyses for irreparable markovian systems, and the additivity theorem is proved. pi（t） is the sum of components in all state transition chains from O to j （see formula（ 2 ））. State O means that the system is good; state j is any state of the system; pi （t） is the probability of the system statejat time tisJ. Some formulas for calculating components are derived （see formulas （12）-（17））. The additivity theorem and the formulas can be used in calculating the reliability of a complex system. Also, they are applicable to calculating the changes of system reliability which are incurred by system age t0 or failure of some units. The method is very convenient for searching the chains and calculating on a computer.