Reliability of a k-out-of-n Cold Standby System with Imperfect Switches

A k-out-of-n standby system is considered where all of its components are s-independent and classified either working or cold standby connected with imperfect switches. The probability density function of the life length for this system is established in closed form, when the underlying components have constant failure rates. Also the reliability function of the system is derived. Finally, the reliability functions for one, two and three out of four systems are deduced for perfect or imperfect switches and identical or non-identical constant failure rates for working and standby components.