Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/17584
標題: 一個具不可信任修理站之可修理系統的貝氏分析
On a repairable system with an unreliable service station: Bayesian approach
作者: 陳又慈
Chen, Yu-Tzu
關鍵字: Availability;可用度;Bayesian estimation;HPD intervals;Mean time to system failure;Simulation;Unreliable service station;貝氏估計;最大事後密度區間;平均故障發生時間;模擬;不可信任之修理站
出版社: 應用數學系所
引用: [1] Agarwal, S. K. and Kalla S. L. (1996). A generalized gamma distribution and its application in reliability. Communications in Statistics -Theory and Methods, 25(1), 201-210. [2] Billinton, R and Pan, J. (1998). Optimal maintenance scheduling in a two identical component parallel redundant system, Reliability Engineering and System Safety 59, 309-316. [3] Birolini, A (1985). The use of stochastic processes in molding reliability problems, Lecture notes in economics and mathematical systems, 252, Springer Verlag, Berlin. [4] Chandrasekhar, P., Natarajan, R. and Yadavalli, V. S. S. (2004). A study on a two unit standby system with Erlangian repair time, Asia-Pacific Journal of Operational Research 21(3), 271-277. [5] De Almeida, A. T. and De Souza, F. M. Campello (1993). Decision theory in maintenance strategy for a 2-unit redundant standby system, IEEE Transactions on Reliability 42(3), 401-407. [6] Goel, L. R. and Shrivastava, P. (1991). Profit analysis of a two-unit redundant system with provision for test and correlated failures and repairs, Microelectronics and Reliability 31, 827-833. [7] Gururajan, M. and Srinivasan, B. (1995). A complex two-unit system with random breakdown of repair facility, Microelectronics and Reliability 35(2), 299-302. [8] Jie, M. (1991). Interval estimation of availability of a series system, IEEE Transactions on Reliability R-40(5), 541-546. [9] Masters, B. N., Lewis, T. O. and Kolarik, W. J. (1992). A confidence interval availability for systems with Weibull operating time and lognormal repair time, Microelectronics and Reliability 32, 89-99. [10] Osaki, S. and Nakagawa, T. (1976). Bibliography for reliability and availability of stochastic systems, IEEE Transactions on Reliability R-25, 284-287. [11] Rajamanickam, S. P. and Chandrasekar, B. (1997). Reliability measures for two-unit systems with a dependent structure for failure and repair times, Microelectronics and Reliability 37(5), 829-833. [12] Seo, J. H., Jang, J. S. and Bai, D. S. (2003). Lifetime and reliability estimation of repairable redundant system subject to periodic alternation, Reliability Engineering and System Safety 80, 197-204. [13] Shi, D. H. and Liu, L. (1996). Availability analysis of a two-unit series system with a priority shut-off rule, Naval Research Logistics 43, 1009-1024. [14] Shi, D.H. and Li, W. (1993). Availability analysis of a two unit series system with shut-off rule and first-fail, first-repaired, Acta Mathematicae Applicatae Sinica 1, 88-91. [15] Sridharan, V. and Mohanavadivu, P. (1998). Some statistical characteristics of a repairable, standby, human & machine system, IEEE Transactions on Reliability 47(4), 431-435. [16] Srinivasan, S. K. and Subramanian, R. (1980). Probabilistic Analysis of Redundant Systems, Lecture Notes in Economics and Mathematical Systems, 175, Springer Verlag, Berlin. [17] Yadavalli, V. S. S., Bekker, A. and Pauw, J. (2005). Bayesian study of a twocomponent system with common-cause shock failures, Asia-Pacific Journal of Operational Research 22(1), 105-119. [18] Yadavalli, V. S. S., Botha, M. and Bekker, A. (2002). Asymptotic confidence limits for the steady-state availability of a two-unit parallel system with preparation time for the repair facility, Asia-Pacific Journal of Operational Research 19, 249-256. [19] Yearout, R. D., Reddy P. and Grosh, D. L. (1986). Standby redundancy in reliability-A review, IEEE Transactions on Reliability R-35, 285-292.
摘要: 
我們考慮一個不可信任的修理站,此系統包含兩台可修護的機器,可藉由貝氏的觀點,對未確定的參數假設具有不同的事前分配。我們假設機器壞掉的間隔時間及修護時間均服從指數分配,而且,修理站故障的間隔時間及修理時間也都服從指數分配。當機器壞掉的間隔時間及修護時間,修理站故障的間隔時間及修理時間都具有不確定性的參數時,我們採用貝氏的方法來評估這整個系統的特徵。本篇論文以蒙地卡羅的方法所得到的事後分配,進一步求得系統的平均故障發生時間及系統在穩態時的可用度的統計推論,最後以一些數值的實驗數據來說明結論。

System characteristics of a two-unit repairable system are studied from a Bayesian viewpoint with different types of priors assumed for unknown parameters, in which the service station is unreliable. Time to failure and time to repair of the operating units are assumed to follow exponential distributions. In addition, the failure time and repair time of service station also follow exponential distributions. When time to failure and time to repair of operating units, failure time and repair time of service
station are with uncertain parameters, a Bayesian approach is adopted to evaluate system characteristics. Monte Carlo simulation is used to derive the posterior distribution for the mean time to system failure and the steady-state availability. Some numerical experiments are performed to illustrate the results derived in this paper.
URI: http://hdl.handle.net/11455/17584
其他識別: U0005-2106200622411900
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