Title: Queueing analysis of two unreliable servers machining system with switching and common cause failure

Authors: Madhu Jain; Chandra Shekhar; Shalini Shukla

Addresses: Department of Mathematics, Indian Institute of Technology, Roorkee, Uttarakhand, 247 667, India ' Department of Mathematics, Birla Institute of Technology and Science, Pilani, Rajasthan, 333 031, India ' Department of Mathematics, DAV (PG) College, Dehra Dun, Uttarakhand, 248 001, India

Abstract: In this paper, we analyse the performance of primary and secondary unreliable servers in a multi-component machining system. For the smooth functioning of the system, there is a provision of warm spares that may not be perfect in switching the failed operating unit. Primary server is prone to complete or partial breakdown whereas secondary server faces only complete breakdown independently or simultaneously due to common cause. The life time and repair time of the operating units, breakdown and the repair time of the servers are exponentially distributed. Various performance indices are formulated to study the behaviour of the queueing model of concerned machining system developed more significantly. By taking an illustration, the sensitivity analysis is carried out. The numerical results are summarised in tabular form and also depicted via graphs.

Keywords: Markovian queues; machine repair; warm spares; switching failure; common cause failure; partial breakdown; queueing modelling; unreliable servers; machining systems; sensitivity analysis.

DOI: 10.1504/IJMOR.2013.054732

International Journal of Mathematics in Operational Research, 2013 Vol.5 No.4, pp.508 - 536

Received: 13 Feb 2012
Accepted: 29 Jun 2012

Published online: 31 Mar 2014 *

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