Abstract: The cold standby redundancy systems with inadequate samples are investigated based on the uncertainty theory. The lifetimes of system elements are assumed to have independent and non-identical uncertainty distributions with uncertain parameters. Three basic models, including a conversion switch with absolutely reliable mode, a conversion switch with discrete mode and a conversion switch with continuous mode, are established for the cold standby redundancy systems based on the reliability function and mean time to failure, respectively. In addition, a special case is analyzed, which lifetime of each element is independent identical uncertainty distribution with uncertain parameters. Finally, numerical examples are given to illustrate the rationalization of the developed models.

Key words: uncertainty theory, reliability, mean time to failure, cold standby system