Markov chain approach to availability and profit evaluation of a series-parallel system with minor and major failures

The paper deals with modeling and performance evaluation of a series-parallel with independent failures using Markov Birth-Death process and probabilistic approach. The system consists of three subsystems arranged in series and parallel configurations with three possible states, working, reduced capacity and failed. Through the transition diagram, systems of differential equations are developed and solved recursively via probabilistic approach. Failure and repair rates for all the subsystems are assumed constant. Availability and profit matrices for each subsystem have been developed to provide various performance values for different combinations of failure and repair rates of all subsystems. Performance of each subsystem of series-parallel system is evaluated. The present study will help the plant management in understanding the optimum system availability and profit to be achieved, and the maintenance efforts needed to maintain an appropriate level of availability and profit and useful for timely execution of proper maintenance improvement, decision, planning and optimization.