Computational analysis of machine repair problem with unreliable multi-repairmen

Authors:
Jau-Chuan Ke;Ying-Lin Hsu;Tzu-Hsin Liu;Zhe George Zhang
Affiliations:
Department of Applied Statistics, National Taichung University of Science and Technology, Taichung 404, Taiwan, ROC;Department of Applied Mathematics, National Chung Hsing University, Taichung 402, Taiwan, ROC;Department of Applied Statistics, National Taichung University of Science and Technology, Taichung 404, Taiwan, ROC and Department of Applied Mathematics, National Chung Hsing University, Taichung ...;Department of Decision Science, College of Business and Economics,Western Washington University, Bellingham, WA 98225-9077, USA and Beedie School of Business, Simon Fraser University, Burnaby, BC, ...
Venue:
Computers and Operations Research
Year:
2013

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Abstract

This paper considers a multi-repairmen problem comprising of M operating machines with W warm standbys (spares). Both operating and warm standby machines are subject to failures. With a coverage probability c, a failed unit is immediately detected and attended by one of R repairmen if available. If the failed unit is not detected with probability 1-c, the system enters an unsafe state and must be cleared by a reboot action. The repairmen are also subject to failures which result in service (repair) interruptions. The failed repairman resumes service after a random period of time. In addition, the repair rate depends on number of failed machines. The entire system is modeled as a finite-state Markov chain and its steady state distribution is obtained by a recursive matrix approach. The major performance measures are evaluated based on this distribution. Under a cost structure, we propose to use the Quasi-Newton method and probabilistic global search Lausanne method to search for the global optimal system parameters. Numerical examples are presented to demonstrate the effectiveness of our approach in solving a highly complex manufacturing system subject to multiple uncertainties.