Abstract
The Monte Carlo method is the general designation for stochastic simulation using random numbers. Monte Carlo is the name of the suburb in Monaco made famous by its gambling casino. The name was also used as the secret code for atomic bomb work performed during World War II involving random simulation of the neutron diffusion process. Monte Carlo methods have been used in many areas since that time.
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References
R. Y. Rubinstein, Simulation and the Monte Carlo Method, Wiley, New York, 1981.
D. H. Lehmer, “Mathematical Methods in Large-Scale Computing Units,” Ann. Comp. Lab., Harvard Univ., 1951, No. 26, pp. 141-146.
B. J. T. Morgan, Computer Simulation and Monte Carlo Method, Chapman and Hall, London, 1984.
Fang Zaigen, Computer Simulation and Monte Carlo Method, Publishing House of Beijing Industrial Institute, 1988.
M. Greenberger, “Notes in a New Pseudo-Random Number Generator,” J. Assoc. Comp. Math., No. 8, 1961, pp. 163–167.
D. E. Knuth, The Art of Computer Programming: Seminumerical Algorithms, Vol. 2, Addison-Wesley, Massachusetts, 1969.
M. Greenberger, “An a Priori Determination of Serial Correlation in Computer Generated Random Numbers,” Math. Comp., No. 15, 1961, pp. 383–389.
A. M. Law and W. D. Kelton, Simulation Modelling and Analysis, McGraw-Hill, New York, 1982.
M. Abramovitz and I. A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, 1968.
G. E. P. Box and M. E. Müller, “A Note on the Generation of Random Normal Deviates,” Ann. Math. Stat., No. 29, 1958, pp. 610–611.
J. M. Hammersley and D. C. Handscomb, Monte Carlo Methods, Wiley, New York, 1964.
A. W. Marshall, “The Use of Multi-Stage Sampling Schemes in Monte Carlo Computations,” in Symposium on Monte Carlo Methods, Wiley, New York, 1956, pp. 123–14.
W. S. Cochran, Sampling Techniques, Wiley, New York, 1966.
J. M. Hammersley and K. W. Morton, “A New Monte Carlo Technique: Antithetic Variates,” Proc. Cambridge Philos. Soc, No. 52, 1956, pp. 449–474.
H. Kumamoto, K. Tanaka, K. Inoue, and E. J. Henley, “Dagger-Sampling Monte Carlo for System Unavailability Evaluation,” IEEE Trans, on Reliability, R-29, No. 2, 1980.
G. Fishman, Principles of Discrete Event Simulation, J. Wiley, New York, 1978.
L. T. Blank, Statistical Procedures for Engineering, Management and Science, McGraw-Hill, New York, 1980.
A. M. Mood, F. A. Graybill, and D. C. Boes, Introduction to the Theory of Statistics, McGraw-Hill, New York, 1974.
S. J. Yakowitz, Computational Probability and Simulation, Addison-Wesley, Massachusetts, 1977.
J. Banks and J. S. Carson, Discrete Event System Simulation, Prentice-Hall, Englewood Cliffs, NJ, 1984.
E. J. Henley and H. Kumamoto, Probabilistic Risk Assessment: Reliability Engineering, Design, and Analysis, IEEE Press, New York, 1992.
R. Billinton and W. Li, “Hybrid Approach for Reliability Evaluation of Composite Generation and Transmission Systems Using Monte Carlo Simulation and Enumeration Technique,” IEE Proc. C, Vol. 138, No. 3, 1991, pp. 233–241.
J. Endrenyi, Reliability Modeling in Electric Power Systems, Wiley, New York, 1978.
J. Kleijnen, Statistical Techniques in Simulation: Part I and II, Marcel Dekker, New York, 1975.
R. Billinton and W. Li, “A System Transition Sampling Method for Composite System Reliability Evaluation,” IEEE Trans, on PS, Vol. 8, No. 3, 1993, pp. 761–770.
L. Gan, “Multi-Area Generation System Adequacy Assessment by Monte Carlo Simulation,” M.Sc. Thesis, University of Saskatchewan, 1991.
R. Billinton and R. N. Allan, Reliability Evaluation of Engineering Systems: Concepts and Techniques (2nd edition), Plenum, New York, 1992.
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© 1994 Springer Science+Business Media New York
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Billinton, R., Li, W. (1994). Elements of Monte Carlo Methods. In: Reliability Assessment of Electric Power Systems Using Monte Carlo Methods. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1346-3_3
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DOI: https://doi.org/10.1007/978-1-4899-1346-3_3
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