MCNP s ten statistical checks in VS .NET

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Appendix: MCNP s ten statistical checks
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MCNP records information on the mean, relative error, variance of the variance, gure of merit, and the tail slope behavior of the empirical score distribution to assist the user in evaluating the Monte Carlo results Statistical check for the mean: a non-monotonic behavior (no up or down trend) in the estimated mean as a function of the number histories N for the last half of the problem
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Statistical checks for the relative error (R) (ie, standard deviation divided by the mean): an acceptable magnitude of the estimated R of the estimated mean (less than 005 for a point detector tally or less than 010 for a non-point detector tally); a monotonically decreasing R as a function of the number histories N for the last half of the problem; a 1/ N decrease in the R as a function of N for the last half of the problem Statistical checks for the variance of the variance (VOV): the magnitude of the estimated VOV should be less than 010 for all types of tallies; a monotonically decreasing VOV as a function of N for the last half of the problem; a 1/N decrease in the VOV as a function of N for the last half of the problem Statistical checks for the gure of merit (fom): a statistically constant value of the fom as a function of N for the last half of the problem; a non-monotonic behavior in the fom as a function of N for the last half of the problem Statistical check for the large score tail slope of the empirical score distribution (f (x)): the slope of the 25 to 201 largest positive history scores x should be greater than 30 so that the second moment x 2 f (x)dx will exist if the slope is extrapolated to in nity The seven N -dependent checks are for the last half of the problem For example, one expects a roughly monotonic decrease in the relative error after enough samples have been run MCNP looks at the sample information from the last half of the samples (N/2 to N ) and if the last half of the problem seems to have the correct dependence, then N is deemed large enough
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References
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[1] GI Bell and S Glasstone Nuclear Reactor Theory Van Nostrand, New York, 1970
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[2] TE Booth Exact Monte Carlo solution of elliptic partial differential equations Journal of Computational Physics, 39: 396 404, 1981 [3] TE Booth A sample problem for variance reduction in MCNP Technical Report LA-10363-MS, Los Alamos National Laboratory, 1985 [4] TE Booth Monte Carlo variance reduction approaches for non-Boltzmann tallies Technical Report LA-12433, Los Alamos National Laboratory, 1992 [5] TE Booth A Monte Carlo variance reduction approach for non-Boltzmann tallies Nuclear Science and Engineering, 116: 113 124, 1994 [6] TE Booth Pulse height tally variance reduction in MCNP Technical Report LA-13955, Los Alamos National Laboratory, 2002 [7] TE Booth Ex post facto Monte Carlo variance reduction Nuclear Science and Engineering, 148: 391 402, 2004 [8] TE Booth A transport process approach to understanding Monte Carlo transport methods Technical Report LA-UR-04-1426, Los Alamos National Laboratory, 2004 [9] TE Booth and KW Burn Some sample problem comparisons between the DSA cell model and the quasi-deterministic method Annals of Nuclear Energy, 29(11): 733 765, 1993 [10] TE Booth, JA Carlson, JA Favorite et al Taking the next step with intelligent Monte Carlo Technical Report LA-UR-00-4892, Los Alamos National Laboratory Report, October 1, 2001 [11] TE Booth and JS Hendricks Importance estimation in forward Monte Carlo calculations Nuclear Technology/Fusion, 5: 90 100, 1984 [12] TE Booth and SP Pederson Unbiased combinations of nonanalog Monte Carlo techniques and fair games Nuclear Science and Engineering, 110: 254 261, 1992 [13] JP Both, A Mazzolo, O Petit, Y Peneliau, and B Roesslinger User manual for version 43 of the TRIPOLI-4 Monte Carlo method particle transport computer code Technical Report CEA-R-6044, CEA/Saclay, France, 2003 [14] KW Burn A new weight-dependent direct statistical approach model Nuclear Science and Engineering, 125: 128 170, 1997 [15] S Chucas and M Grimstone The acceleration techniques used in the Monte Carlo code MCBEND 8th International Conference on Radiation Shielding, Arlington, TX, USA, 25 28 April 1994 [16] DH Davis Critical-size calculations for neutron systems by the Monte Carlo method Technical Report UCRL-6707, Lawrence Radiation Laboratory, December 12, 1961 [17] CM Diop, O Petit, E Dumonteil, FX Hugot, YK Lee, A Mazzolo, and JC Trama Tripoli-4: A 3D continuous-energy Monte Carlo transport code First International Conference on Physics and Technology of Reactors and Applications, Marrakech, March 14 16, 2007, GMTR (2007) [18] A Dubi and DJ Dudziak Optimal choice of parameters for exponential biasing in Monte Carlo Nuclear Science and Engineering, 70: 1 13, 1979 [19] BL Fox Strategies for Quasi-Monte Carlo Kluwer Academic, Boston, 1999
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