In this paper we discuss about the Availability of the various systems of process industries. As we know Availability is highly dependent on failure rate and repair rate. By using Markove Death Birth Rule we can generate transition diagrams for various systems. Transition diagram represent the all stages of systems and subsystems. The main three states of any system are-full working state, reduced capacity state, failed state. After the performance modeling of the systems the availability is calculated. By using Programming we can find out the different values of availability by varying failure rate and repair rate. In this way the critical system or subsystem can be identified.