Reliability analysis of a system with a mixture of warm and cold standby

A single-server two-unit standby system with two modes of each unit—normal and total failure—is considered. The standby units are repeatedly interconverted after a random time from warm to cold and cold to warm. Upon failure of the operative unit, the standby unit, if it is warm, starts to operate instantaneously; otherwise, the system goes down until the cold standby starts to operate. System failure occurs when both units fail totally. Identifying the system at suitable regenerative epochs, the integral equations are set up and the expressions for reliability and mean time to system failure (MTSF) are obtained. The graphical behaviour of MTSF is also studied in a particular case.