Vacation model for Markov machine repair problem with two heterogeneous unreliable servers and threshold recovery

Subject Areas : Mathematical Optimization

Madhu Jain ¹ , Rakesh Kumar Meena ²

1 - Department of Mathematics, IIT Roorkee, Roorkee, India
2 - Department of Mathematics, IIT Roorkee, Roorkee, India

Received: 2020-10-06 Accepted : 2020-10-06 Published : 2018-03-01

Keywords: Threshold policy . Vacation . Machine repair . Cost optimization . Runge, Kutta method . ANFIS,

Abstract :

Markov model of multi-component machining system comprising two unreliable heterogeneous servers and mixed type of standby support has been studied. The repair job of broken down machines is done on the basis of bi-level threshold policy for the activation of the servers. The server returns back to render repair job when the pre-specified workload of failed machines is build up. The first (second) repairman turns on only when the work load of N1(N2) failed machines is accumulated in the system. The both servers may go for vacation in case when all the machines are in good condition and there are no pending repair jobs for the repairmen. Runge–Kutta method is implemented to solve the set of governing equations used to formulate the Markov model. Various system metrics including the mean queue length, machine availability, throughput, etc., are derived to determine the performance of the machining system. To provide the computational tractability of the present investigation, a numerical illustration is provided. A cost function is also constructed to determine the optimal repair rate of the server by minimizing the expected cost incurredon the system. The hybrid soft computing method is considered to develop the adaptive neuro-fuzzy inference system (ANFIS). The validation of the numerical results obtained by Runge–Kutta approach is also facilitated by computational results generated by ANFIS.