Abstract: The universal generating function (UGF) is an important approach to the analysis of the reliability of a multi-state system. By decomposition operators, the expansion of the UGF of a load is obtained, and the reliability of a multi-state system is calculated using the inner product operator and the UGF of strength when the common cause failure is taken into account. Reliability models of a multi-state system are established considering the effect of times of load and multi-loads. The influence of the common cause failure and the times of load on the reliability of a multi-state system is studied by an example. The results show that the reliability of a multi-state system and its components is influenced by the common cause failure and times of load, and system reliability decreases obviously when the times of load increase. When the times of load are designated and a common cause failure exists, the reliability of a multi-state system can be calculated directly by means of the model proposed.

Key words: universal generating function, reliability, model, multi-state system, common cause failure