FUZZY ANALYSIS OF MACHINE REPAIR PROBLEM WITH SWITCHING FAILURE AND REBOOT

  • Chandra Shekhar Department of Mathematics, Birla Institute of Technology and Science, Pilani, Rajasthan-333 031 (India)
  • Madhu Jain Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand-247 667 (India)
  • Madhu Jain Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand-247 667 (India)
  • Siddharth Bhatia Birla Institute of Technology and Science, Pilani, Rajasthan-333 031(India)
Keywords: Availability, fuzzy set, membership function, machine repair problem, cold standby, switching failure, reboot delay

Abstract

Multi-component machining systems are being used in every sphere of engineering sector such as job shops, flow lines, communication system, computer system, etc. This paper presents fuzzy analysis of availability characteristics of machining system comprising of multiactive units and multi-standby units. The Markov machine repair model has been developed by incorporating the concepts of switching failure and reboot. The life times of identical active units and identical standby units follow the fuzzified exponential distribution. The time-to-repair of failed unit is also governed by the fuzzified exponential distribution. The automatic switching of standby unit to replace the failed units may not be perfect in many realistic scenarios as we assume the switching failure probability. The system may reboot itself automatically if the active unit fails and available standby unit is not able to replace the failed unit perfectly. We employ the parametric non-linear program with -cut approach to establish the membership function of availability of the system and availability of both standbys. A numerical example is also provided to validate the suggested approach which facilitates more useful information for the designers and practitioners to examine general repairable system more accurately.

 

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Published
2014-01-29
Section
Articles