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The objective of this paper is to establish some reliability models for redundant systems based on the assumption that the conversion switches are imperfect and distribution parameters are uncertain variables. Some new concepts of random uncertain distributions associated with random uncertain variables are proposed, which are applied to redundant series-parallel systems, including cold redundant system and warm redundant system. In each type of redundant system, we consider two methods to describe the switch lifetimes: random uncertain 0-1 switch lifetime and random uncertain geometric switch lifetime. The reliability and the mean time to failure of these systems are analyzed. Some numerical examples are presented to demonstrate the proposed reliability models and perform a comparison for the system models with uncertain parameters and constant parameters. [ABSTRACT FROM AUTHOR]