MARKOV MODEL FOR SWITCHING FAILURE OF WARM SPARES IN MACHINE REPAIR SYSTEM

  • Madhu Jain Department of Mathematics, Indian Institute of Technology, Roorkee, Uttarakhand, 247667 (INDIA).
  • Chandra Shekhar Department of Mathematics, Birla Institute of Technology and Science, Pilani, Rajasthan, 333031 (INDIA).
  • Shalini Shukla Department of Mathematics, DAV (PG) College, Dehra Dun, Uttarakhand, 248001 (INDIA)
Keywords: Machine Repair, Spares, Vacation, Heterogeneous Servers, Switching Failure, Queue Size Distribution

Abstract

In this investigation, we study the performance characteristics of (m,M) machining systems having warm spares and two heterogeneous servers. The first server is permanent and available full time in the system, whereas the second server takes vacation according to the specific threshold policy. In some real time systems, spares may or may not replace/switch in the system whenever an operating unit failure occurs, as such switching failure has been incorporated. In this paper, we consider a two dimensional continuous time finite state space Markov chain. The steady state queue size distribution for the Markovian machine repair problem, considering switching failure, is obtained computationally using matrix method based on successiveover relaxation. We derive various system characteristics namely, expected number of failed machines in the system, throughput of the system, probability that the server is on vacation, etc. In order to gain maximum net profit, a cost function is constructed in terms of different cost elements to determine the optimal threshold level for the server vacation. For illustration purpose, numerical results are provided. In order to examine the effects of system parameters, the sensitivity analysis has also been facilitated.

 

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Published
2014-01-29
Section
Articles