Modelling and analysis of Markovian continuous flow systems with a finite buffer (original) (raw)

Markov model provides great flexibility in modelling the timing of events. Markov analysis is a method of analysis that can be applied to both repairable and nonrepairable types of systems. In this paper, Markov modelling technique is used to compute the reliability for non-repairable system and defined the mean time to failure of non-repairable systems with different failure rates. This technique is also used to compute the steady-state availability for repairable systems and to derived the mean time between failure of repairable systems with different failure rates and repair rates. Keywords— Markov model; Repairable and Non-repairable systems; MTTF; MTBF; Failure rate; Repair rate; Reliability; INTRODUCTION Markov analysis is the mathematical abstractions to model simple or complex concepts in quite easily computable form. The Markov analysis is also considered powerful modelling and analysis tool in solving reliability tribulations. Markov analysis is a tool for modelling comple...

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 ...

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.