Title: Transient analysis of machining system with spare provisioning and geometric reneging

Authors: Chandra Shekhar; Madhu Jain; Ather Aziz Raina

Addresses: Department of Mathematics, Birla Institute of Technology and Science, Pilani Campus, Pilani, Rajasthan 333 031, India ' Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand 247 667, India ' Department of Mathematical Sciences, BGSB University, Rajouri, J and K 185 234, India

Abstract: In this investigation, we deal with the transient analysis of repairable machining system having multi identical online and warm standby machines. There is facility of repair of failed machines rendered by an unreliable server who is prone to failure and follows the threshold policy in rendering the service and being repaired. The failed machines waiting in the queue may renege and opt sequentially whether to leave the queue or remain in the queue in geometric fashion at the epochs of availability of secondary server. By constructing the transient differential difference equations, the probabilities associated with the system states are determined using the numerical method based on Runge-Kutta method. Various queueing and reliability indices viz. expected number of failed machines in the system, throughput, reliability, mean time to failure, failure frequency, etc., are established and numerically computed by taking illustration. The sensitivity analysis and numerical simulation are performed for exploring the effects of parameters on some performance measures.

Keywords: transient; threshold policy; geometric reneging; machine repair; reliability; queue length.

DOI: 10.1504/IJMOR.2017.087215

International Journal of Mathematics in Operational Research, 2017 Vol.11 No.3, pp.396 - 421

Received: 14 Nov 2015
Accepted: 19 Feb 2016
Published online: 11 Oct 2017 *

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