Markov Chain Profit Modelling and Evaluation between Two Dissimilar Systems under Two Types of Failures

The present paper deals with profit modelling and comparison between two dissimilar systems under two types of failures based on Markovian Birth-Death process. Type I failure is minor in the sense that the work is in a reduced capacity whereas type II failure is major because it causes the entire system failure. Both systems consist of four subsystems arranged in series-parallel with three possible states: working with full capacity, reduced capacity and failed state. The systems are attended to by two repairmen in tandem. Through the transition diagrams, systems of differential difference equations are developed and solved recursively to obtain the steady-state availability, busy period of repair men, and profit function. Profit matrices for each subsystem have been developed for different combinations of failure and repair rates. Furthermore, we compare the profit for the two systems and find that system I is more profitable than system II.