Title: Cost analysis of a machine repair problem with standby, working vacation and server breakdown

Authors: Madhu Jain; Preeti

Addresses: Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, India ' Faculty of Humanity, Physical and Mathematical Sciences, Shobhit University, Meerut-250110, India

Abstract: This paper investigates a machine repair model with standbys, working vacation and server breakdown. As soon as an operating unit fails, it is immediately replaced by a standby unit for the smooth running of the production. When there is no failed unit in the system, the server goes on vacation; meanwhile, the server performs some works and is said to be on working vacation. The life time and the repair time of the units are assumed to be exponentially distributed. The matrix recursive method is used to evaluate various performances measures such as the expected number of failed units in the system, the expected number of operating units in the system, machine availability, operating utilisation, etc. The cost function is established to maximise the gain. The sensitivity analysis is also carried out to examine the effect of different parameters on various system characteristics.

Keywords: working vacation; standby; matrix recursive technique; cost function; server breakdown; queue size; machine repair problem; working vacation.

DOI: 10.1504/IJMOR.2014.063156

International Journal of Mathematics in Operational Research, 2014 Vol.6 No.4, pp.437 - 451

Received: 27 Jul 2012
Accepted: 22 Feb 2013
Published online: 26 Jul 2014 *

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