Stochastic behaviour of a two-unit redundant system with switchover time

There is a two-unit standby redundant system. Standby is kept in cold state. Whenever one unit is operating and the other is in the waiting standby state, switching is initiated on the latter after a random time. If the operative unit fails before the time to initiate switching action on the waiting standby unit, the system fails and the failed unit immediately undergoes repair type 2 along with the switching. However, if the operative unit fails when the other unit is as standby (after switchover), the failed unit undergoes repair type 1 and the unit as standby takes over the operation. All the distributions are arbitrary except failure-time, which is exponential.The system is defined with the help of states which generate a pseudo semi-Markov process. Abundant use of results from the theory of SMP has been made to obtain a large number of parameters which measure reliability characteristics of the system viz. MTSF, steady-state availability, expected number of visits to a state, conditional transition probabilities, first passage time distributions, expected profit rate, etc. Numerical examples are included to illustrate the results.