Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/17997
標題: M/M/R機器修理問題含有第二選擇修理之成本分析
Cost Analysis of the M/M/R Machine Repair Problem with Second Optional Repair
作者: 廖春雯
Liao, Chun-Wen
關鍵字: cost
成本
first essential repair
second optional repair
matrix-geometric method
第一主要修理
第二選擇修理
矩陣-幾何法
出版社: 應用數學系所
引用: [1] J. Al-Jararha and K.C. Madan. An M/G/1 queue with second optional service with general service time distribution. Information and Management Sciences 14 (2), 47-56 (2003). [2] A.O. Allen. Probability, Statistics and Queueing Theory with Computer Science Applications, Academic Press, New York (1978). [3] H. Ashcroft. The productivity of several machines under the care of one operator. Journal of the Royal Statistical Society B 12, 145-151 (1950). [4] F. Benson and D.R. Cox. The productivity of machines requiring attention at random intervals. Journal of the Royal Statistical Society B 13, 65-82 (1951). [5] D.B. Bunday and R.E. Scraton. The G/M/r machine interference model. European Journal of Operational Research 4, 399-402 (1980). [6] J. E. Hilliard. An approach to cost analysis of maintenance float systems. AIIE Transactions, 8, 128-133 (1976). [7] K.C. Madan. An M/G/1 queue with second optional service. Queueing Systems 34, 37- 46 (2000). [8] D.G. Maritas and D.A. Xirokostas. The M/ /r machine interference model: steady state equations and numerical solutions. European Journal of Operational Research 1, 112-123 (1977). [9] J. Medhi. A single server Poisson input queue with a second optional server. Queueing Systems 42, 239-242 (2002). [10] M.F. Neuts. Matrix Geometric Solutions in Stochastic Models. The John Hopkins University Press, Baltimore, 1981. [11] B.D. Sivazlian and K.H. Wang. Economic analysis of the M/M/R machine repair problem with warm standbys. Microelectronics and Reliability 29, 25-35, (1989). [12] J. Sztrik. On the finite-source G/M/r queue. European Journal of Operational Research 20, 261-268 (1985). [13] J. Wang. An M/G/1 queue with second optional service and server breakdowns. Computers and Mathematics with Applications 47, 1713-1723 (2004). [14] K.H. Wang, J.B. Ke and J.C. Ke. Profit analysis of the M/M/R machine repair problem with balking, reneging, and standby switching failures. Computers and Operations Research 34, 835-847 (2007). [15] K.H. Wang and M.Y. Kuo. Profit analysis of the M/ /1 machine repair problem with a non-reliable service station. Computers and Industrial Engineering 32, 587-594 (1997). [16] J.A. White, J.W. Schmidt and G.K. Benett. Analysis of Queueing System. Academic Press, New York (1975).
摘要: 此篇論文分析 M/M/R機器修理問題,修理者可提供主要選擇與第二選擇的兩種修理模式。我們假設機器損壞時間呈指數分配,修理者的第一主要修理與第二選擇修理皆服從指數分配。每一個壞掉的機器到達系統時均須先接受主要修理,並在完成主要修理後有 (1-theta)的機率會離開系統,或有theta的機率會繼續進行第二選擇修理。我們使用矩陣-幾何法求得穩態機率值。接著建立一個成本函數,在維持特定的系統有效水準之下,找出最佳的修理者個數,同時也找出第一和第二修理效率之聯合最佳解。另外我們使用直接找尋的方法和牛頓法在滿足系統有效限制下,得到最小的成本值。
This thesis analyzes the M/M/R machine repair problem with second optional repair. Failure times of the operating machines follow an exponential distribution. Repair times of the first essential repair and the second optional repair are assumed to follow exponential distributions. A failed machine may leave the system either after the first essential repair with probability (1-theta) or at the completion of first essential repair may instantly select to repair for second optional repair with probability theta.We obtain the steady-state solutions through matrix-geometric method. A cost model is derived to determine the optimal number of the repairmen, and the optimal values of the first essential repair rate and the second optional repair rate simultaneously, while maintain the system availability at a specified level. We use the direct search method and the Newton-Quasi method to obtain the global minimum value until the system availability constraint is satisfied.
URI: http://hdl.handle.net/11455/17997
其他識別: U0005-1706200817550600
文章連結: http://www.airitilibrary.com/Publication/alDetailedMesh1?DocID=U0005-1706200817550600
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