N-policy for a repairable redundant machining system with controlled rates

¹ Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667 Uttarakhand, India.
drmadhujain.iitr@gmail.com
² Department of Mathematics, Birla Institute of Technology and Science, Pilani, 333031 Rajasthan, India.
chandrashekhar@pilani.bits-pilani.ac.in
³ Department of Mathematics, D.A.V. (PG) College, Dehra Dun, 248001 Uttarakhand, India.
sshukla.dav@gmail.com

Received: 23 February 2015
Accepted: 6 September 2015

Abstract

The present investigation deals with a multi-component machining system operating under N-policy. There is a provision of k type of mixed standbys units and maintenance crew consisting of permanent repairman as well as removable additional repairmen. The life time and repair time of the units are exponentially distributed with interdependent rates. The permanent repairman can start the repair only when N failed units are accumulated in the system. As soon as a unit fails, it is replaced by an available standby unit. In case when all the standby units are exhausted, the machining system starts to function in a degraded mode due to overload. Markov model is developed by constructing the governing transient state equations which are solved by using Runge−Kutta method. Various performance measures viz. queue size distribution, expected number of failed units, cost function, etc. are evaluated. By taking numerical illustration, numerical results are computed and also depicted with the help of graphs and figures.