Journal of Mechanical Science and Technology

, Volume 24, Issue 6, pp 1211–1218 | Cite as

Choosing a suitable sample size in descriptive sampling



Descriptive sampling (DS) is an alternative to crude Monte Carlo sampling (CMCS) in finding solutions to structural reliability problems. It is known to be an effective sampling method in approximating the distribution of a random variable because it uses the deterministic selection of sample values and their random permutation,. However, because this method is difficult to apply to complex simulations, the sample size is occasionally determined without thorough consideration. Input sample variability may cause the sample size to change between runs, leading to poor simulation results. This paper proposes a numerical method for choosing a suitable sample size for use in DS. Using this method, one can estimate a more accurate probability of failure in a reliability problem while running a minimal number of simulations. The method is then applied to several examples and compared with CMCS and conventional DS to validate its usefulness and efficiency.


Crude Monte Carlo sampling Descriptive sampling Reliability Sample size 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    D. H. Evans, An application of numerical integration techniques to statistical tolerancing, Technometrics, 9(3) (1967) 441–456.CrossRefMathSciNetGoogle Scholar
  2. [2]
    H. S. Seo and B. M. Kwak, Efficient statistical tolerance analysis for general distributions using three-point information, International Journal of Production Research, 40(4) (2000) 931–944.CrossRefGoogle Scholar
  3. [3]
    J. H. Min, Reliability analysis technique using local approximation of cumulative distribution Function, MS. Thesis, Hanyang University, Korea, (2005).Google Scholar
  4. [4]
    A. D. Kiureghian, H. Z. Lin and S. J. Hwang, Second order reliability analysis approximations, Journal of Engineering Mechanics, 113(8) (1987) 1208–1225.CrossRefGoogle Scholar
  5. [5]
    B. Fiessler, H. J. Neumann and R, Rackwitz, Quadratic limit states in structural reliability, Journal of Engineering Mechanics, 1095(4) (1979) 661–676.Google Scholar
  6. [6]
    C. A. Cornell, A probability-based structural code, Journal of the American Concrete Institute, 66(12) (1969) 974–985.Google Scholar
  7. [7]
    O. S. Lee, D. H. Kim and Y. C. Park, Reliability of structures by using probability and fatigue theories, Journal of Mechanical Science and Technology, 22(4) (2008) 672–682.CrossRefGoogle Scholar
  8. [8]
    S. J. Yoon and D. H. Choi, Reliability-based design optimization of slider air bearings, Journal of Mechanical Science and Technology, 18(10) (2004) 1722–1729.Google Scholar
  9. [9]
    A. H. Ang and W. H. Tang, Probability concepts in engineering planning and design, John Wiley & Sons, New York, USA, (1984).Google Scholar
  10. [10]
    A. Harbitz, An efficient sampling method for probability of failure calculation, Structural Safety, 3 (1986) 109–115.CrossRefGoogle Scholar
  11. [11]
    N. P. Buslenko, D. I. Golenko, Y. A. Shreider, I. M. Sobol and V. G. Sragowich, The Monte Carlo method, Pergamon Press, New York, USA, (1964).Google Scholar
  12. [12]
    M. L. Shooman, Probability reliability: An engineering approach, McGraw-Hill, New York, USA, (1968).Google Scholar
  13. [13]
    R. E. Melcher, Structural reliability: Analysis and Prediction, Ellis Horwood, (1987).Google Scholar
  14. [14]
    E. Saliby, A reappraisal of some simulation fundamentals, Ph.D. Thesis, University of Lancaster, (1980).Google Scholar
  15. [15]
    E. Saliby, Descriptive sampling: A better approach to Monte Carlo simulation, Journal of the Operational Research Society, 41(12) (1990) 1133–1142.Google Scholar
  16. [16]
    E. Saliby, Rethinking simulation: descriptive sampling, Sao Paulo: Atlas/EDUFRJ, Portuguese, (1989).Google Scholar
  17. [17]
    G. S. Fishman, Monte-Carlo: Concepts, algorithms and applications, Springer-Verlag, (1997).Google Scholar
  18. [18]
    K. W. Ross, D. Tsang and J. Wang, Monte-Carlo summation and integration applied to multichain Queueing networks, Journal Association Computer Machine, 41(6) (1994) 1110–1135.MATHMathSciNetGoogle Scholar
  19. [19]
    K. Ziha, Descriptive sampling in structural safety, Structural Safety, 17 (1995) 33–41.CrossRefGoogle Scholar
  20. [20]
    B. A. Cullimore, Dealing with uncertainties and variations in thermal design, Proceedings of InterPack ′01 Pacific Rim International Electronic Packaging Conference, Kauai, Hawaii (2001).Google Scholar
  21. [21]
    D. J. McCormick and J. R. Olds, A design of experiments-based method for point selection in approximating output distributions, 2002 AIAA/ISSMO Symposium on Multidisciplinary Analysis and Design Optimization, Atlanta, GA (2002).Google Scholar
  22. [22]
    E. Saliby and F. Pacheco, An empirical evaluation of sampling methods in risk analysis simulation: Quasi-Monte Carlo, descriptive sampling and Latin Hypercube Sampling, Proceedings of the 2002 Winter Simulation Conference, 1606–1610 (2002).Google Scholar
  23. [23]
    J. Staum, S. Ehrlichman and V. Lesnevski, Work reduction in financial simulations, Proceedings of the 2003 Winter Simulation Conference (2003).Google Scholar
  24. [24]
    R Development Core Team, R(ver. 2.6.1):A language and environment for statistical computing, R Foundation for statistical computing, Vienna, Austria, URL, (2007).
  25. [25]
    E. Saliby, Understanding the variability of simulation estimates: an empirical study, Journal of the Operational Research Society, 41 (1990) 319–327.Google Scholar
  26. [26]
    E. Saliby and R. J. Paul, Implementing descriptive sampling in three-phase discrete event simulation models, Journal of the Operational Research Society, 44 (1993) 147–160.MATHGoogle Scholar
  27. [27]
    E. Saliby, Input sample size determination when using descriptive sampling, Proceedings 13th International Conference ITI-1991, Dubrovnik, Croatia (1991).Google Scholar
  28. [28]
    L. Wang and R. V. Gradhi, Efficient safety index calculation for structural reliability analysis, Computer and Structures, 52(1) (1994) 103–111.MATHCrossRefGoogle Scholar
  29. [29]
    Southwest Research Institute, Probabilistic structural analysis methods (PSAM) for select space propulsion systems components, NESSUS Version 6.0 release notes, (1992).Google Scholar
  30. [30]
    H. Madsen, S. Krenk and N. Lind, Methods of structural safety, Prentice-Hall, (1986).Google Scholar

Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of MathematicsKorea Air-Force AcademyChungbukKorea
  2. 2.School of Mechanical EngineeringHanyang UniversitySeoulKorea
  3. 3.Department of Mathematics and Research Institute for Natural SciencesHanyang UniversitySeoulKorea

Personalised recommendations