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Cost Analysis of the Warm-Standby M/M/R Machine Repair Problem with Server Partial Breakdowns and Delay Repair
|關鍵字:||成本分析;cost analysis;服務者部分故障;延遲修理;暖備用機器;機率全域搜索;server partial breakdowns;delay repair;warm standby machine;Probability global search Lausanne||出版社:||統計學研究所||引用:|| F. Benson and D. R. Cox. “The productivity of machines requiring attention at random intervals.” Journal of the Royal Statistical Society, 13 (1951): 65-82.  B. Raphael and I.F.C Smith. “A direct stochastic algorithm for global search.” Applied Mathematics and Computation, 146 (2003): 729-758.  S. C. Albright. “Optimal maintenance-repair policies for the machine repair problem.” Naval Research Logistics Quarterly, 27 (1980): 17-27.  G. Feichtinger. “Optimal repair policy for a machine service problem.” Optimal Control Applications and Methods, 3 (1982): 15-22.  J. Wang. “Probabilistic analysis and multi-criteria decision for machine assignment problem with general service times.” Systems Engineering and Electronics, 5 (1994): 53-61.  S. K. Singh and G. C. Sharma. “Markovian analysis of the Mx/Ek/1 machine repair problem with spares.” Microelectronics Reliability, 33 (1993): 493-495.  K.-H. Wang and B. D. Sivazian. “Cost analysis of the M/M/R machine repair problem with spares operating under variable service rates.” Microelectronics Reliability, 32 (1992): 1171-1183.  K.-H. Wang and M.-Y. Kuo. “Profit analysis of the M/Ek/1 machine repair problem with a non-reliable service station.” Computers and Industrial Engineering, 32 (1997): 587-594.  K.-H. Wang and B. D. Sivazian. “Comparative analysis for the G/G/R machine repair problem.” Computers and Industrial Engineering, 18 (1990): 511-520.  F. Zhang and J. Wang. “Equilibrium analysis of the observable queue with balking and delayed repairs.” Computational Science and Optimization (CSO), 2 (2010): 125-129.  Y. Jiang and X. Meng. “An optimal replacement policy for the alpha series system with single vacation and delay repair.” Multimedia Technology (ICMT), (2011): 2408-2410.  G. Chao, Q. Xing and M. Dan. “Reliability of two-dissimilar-unit parallel system with delay in repair.” Control Conference (CCC), (2012): 1307-1312.  J.-C. Ke, Y.-L. Hsu, T.-H. Liu and Z.-G. Zhang. “Computational analysis of machine repair problem with unreliable multi-repairmen.” Computers and Operations Research, 40 (2013): 848-855.  S. Ghosh and P. P. Mujumdar. “Risk minimization in water quality control problems of a river system.” Advances in Water Resources, 29 (2006): 458-470.  A. Patil, R. Langoju and P. Rastogi. “Phase shifting interferometry using a robust parameter estimation method.” Optics and Lasers in Engineering,45 (2007): 293-297.||摘要:||
This paper investigates the warm-standby M/M/R machine repair problem with server partial breakdowns and delay repair. When an operating machine (or warm standby) fails, it may be immediately detected, located, and replaced. The server can partial break down at any time but he still can serve. The partial broken down servers will be delay repaired. Firstly, we use a matrix-form method to derive the steady-state probabilities, using which various system performance measures that can be obtained. Secondly, a cost model is developed and we use the Probability global search Lausanne to find the optimal value of servers and warm standbys (R,S) , say (R*,S*) , and the optimal value of two kinds of service rate (mu_w,mu_d) , say (mu_w*,mu_d*) at the minimum cost. Finally, numerical results are provided in which various system performance measures are calculated under optimal operating conditions. Sensitivity analysis is also investigated.
|Appears in Collections:||統計學研究所|
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