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Comparative Analysis of System with Warm Standbys, Detection Delay, Standby Switching Failure, Reboot Delay and General Repair Times
|關鍵字:||unavailability;偵測延遲;detection delay;standby switching failures;reboot delay;supplementary variable;備用轉換失敗;啟動延遲;輔助變數技巧||出版社:||應用數學系所||引用:|| Arnold, T.F. (1973), The concept of coverage and its effect on the reliability model of repairable system, IEEE transactions on computers, C-22: 252-254.  Bouricius, W.G.., Carter, W.C. and Rchneider, P.R. (1969), Reliability modeling techniques for self-repairing computer system, Proceedings, 24th National Conference of the ACM, pp. 295-309.  Cohen, J.W. (1969), The single server queue, North-Holland, Amsterdam, 1969.  Cox, D.R. (1955), The analysis of non-Markovian stochastic processes by the inclusion of supplementary variable, Proceedings of the Cambridge Philosophical Society, 51:433-441.  Dugan, J.B. and Trivedi, K.S. (1989), Coverage modeling for dependability analysis of fault-tolerant system, IEEE transactions on computers, 38(6): 775-787.  Galikowsky, C., Sivazlian, B.D., Chaovalitwongse, P. (1996), Optimal redundancies for reliability and availability of series systems, Microelectronics and Reliability, 36: 1537-1546.  Gupta, U.C., Rao, TSS S. (1994), A recursive method compute the steady state probabilities of the machine interference model: (M/G/1)/K, Computers and Operations Research, 21: 597-605.  Gupta, U.C., Rao, TSS S. (1996), On the M/G/1 machine interference model with spares, European Journal of Operational Research, 89: 164-171.  Hokstad, P. (1975), A supplementary variable technique applied to the M/G/1 queue, Scandinavian Journal of Statistics, 2: 95-98.  Ke, J.B., Lee, W.C. and Wang, K.H. (2007), Reliability and sensitivity analysis of a system with multiple unreliable service stations and standby switching failures, Physica A, 380: 455-469.  Keilson, J. and Kooharian, A. (1960), On time dependent queueing processes, The Annals of mathematical statistics, 31:104-112.  Lewis, E.E. (1996), Introduction to reliability engineering, 2nd Edition, Wiley & Sons, New York..  Scheneidewind, N.F. (2000), Modeling the fault correction process, Proceedings of the 12th International Symposium on Software Reliability Engineering, pp. 185-190.  Sivazlian, B.D. and Wang, K.H. (1989), Economic analysis of the M/M/R machine repair problem with warm standbys, Microelectronics and Reliability, 29: 23-35.  Takacs, L. (1963), Delay distributions for one line with Poisson input, general holding times and various orders of service, Bell System Technical Journal, 42:487-504.  Trivedi, K.S. (2002), Probability and statistics with reliability, queuing and computer science applications, 2nd Edition. John Wiley & Sons, New York.  Wang, K.H. and Ke, J.C. (2003), Probabilistic analysis of a repairable system with warm standbys plus balking and reneging, Applied Mathematical Modelling, 27: 327-336.  Wang, K.H. and Pearn, W.L. (2003), Cost benefit analysis of series systems with warm standby components, Mathematical Methods of Operations Research, 58: 247-258.  Wang, K.H., Liou, Y.C. and Pearn, W.L. (2005), Cost benefit analysis of series systems with warm standby components and general repair times, Mathematical Methods of Operations Research, 61: 329-343.  Wang, K.H., Chiu, L.W. (2006), Cost benefit analysis of availability systems with warm standby units and imperfect coverage, Applied Mathematics and Computation, 172(2): 1239-1256.  Wang, K.H., Dong, W.-L., Ke J.-B. (2006), Comparing of reliability and the availability between four systems with warm standby components and standby switching failures, Applied Mathematics and Computation, 183: 1310-1322.  Wang, K.H., Ke, J.B, and Ke, J.C. (2007), Profit analysis of the M/M/R machine repair problem with balking, reneging and standby switching failures, Computers and Operations Research, 34: 835-847.  Xie, M. and Zhao, M. (1992), The Schneidewind software reliability model revisited, Proceedings of 3rd International Symposium on Software Reliability Engineering, pp.184-192.||摘要:||
在本篇研究中，我們取四種具有暖備備用零件的系統來進行討論。其中，這些系統都具有偵測延遲、備用轉換失敗率與啟動延遲的特性。主要零件和備用零件的故障率與修復率分別為指數分配與一般分配。重新啟動時間和偵測時間則都服從指數分配。假設在備用零件轉換成主要零件的過程中，其發生轉換失敗的機率為q。我們利用有系統的矩陣方法與輔助變數技巧，針對四種不同的結構，推導出穩態的無效度(UAv)。對於這四種結構，我們提供了三種不同的修復時間分配，如：指數分配、3-stage Erlang 分配、deterministic 分配。最後，我們代入不同的數值，來分析這四種結構的特性。
In this thesis, we discuss the unavailability characteristics among four different configurations with warm standby units in which detection delay, standby switching failures and reboot delay are considered. The four configurations are studied under the assumption that the time-to-breakdown and time-to-repair of active (or standby) units are exponentially and generally distributed, respectively. The detection rate and the reboot rate are assumed to be exponentially distributed with parameter and , respectively. It is assumed that the process in switching a standby unit to be an active unit may experience a failure probability of q. We provide a systematic matrix method, using the supplementary variable technique to develop the steady-state unavailability, UAv, for four configurations and perform comparisons with three various repair time distributions, such as exponential, k-stage Erlang and deterministic. The sensitivity analyses for UAv with each parameter of the system are also studied.
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