TECHNICAL PAPERS
Feb 1, 1996

Statistical Implications of Methods of Finding Characteristic Strengths

Publication: Journal of Structural Engineering
Volume 122, Issue 2

Abstract

Various statistical methods of estimating the characteristic strengths of materials or structural components from the results of experimental tests can be assessed in the figures and tables of this paper. The methods are tested on normal, log-normal, and two-parameter Weibull populations as well as data sets from timber engineering activities. The results show how the required sample size depends on the coefficient of variation and the likely errors if an incorrect distribution is assumed. Two statistical methods that effectively fit distributions to the lower tails of experimental results, with the consequence that the estimations of characteristic strength are relatively insensitive to the form of the underlying distribution, are recommended because their estimations are almost as good as those obtained when the form of the underlying distribution is known. These methods also have the practical advantage that testing can be stopped when all members of a sample have been loaded to a level so that about 10% have failed, leaving 90% undamaged.

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References

1.
Bain, L. J., and Engelhardt, M.(1981). “Simple approximate distributional results for confidence and tolerance limits for Weibull distributions based on maximum likelihood estimators.”Technometrics, 23(1), 15–20.
2.
Bury, K. V. (1975). Statistical models for applied science . John Wiley & Sons, Inc., New York, N.Y.
3.
Cochran, W. G., Mostellier, F., and Tukey, J. W. (1954). “Principles of sampling.”J. Am. Statistical Assoc., 54(Mar.), 13–35.
4.
Conover, W. J. (1980). Practical nonparametric statistics, 2nd Ed., John Wiley & Sons, Inc., New York, N.Y.
5.
Green, W. G., and Evans, J. W. (1988). “Evaluating lumber properties: practical concerns and theoretical restraints.”Proc., 1988 Int. Conf. on Timber Engrg., Forest Products Res. Soc., Madison, Wis., 203–217.
6.
Hunt, R. D. (1990). “Investigations into the bending and tension strength of finger jointed machine stress graded timber.”Timber Engrg. Rep., Dept. of Civ. Engrg., Univ. of Auckland, Auckland, New Zealand.
7.
Hunt, R. D., and Bryant, A. H. (1994). “Investigations of methods used to obtain lower tolerance bounds.”School of Engrg. Rep. No. 54b, Univ. of Auckland, Auckland, New Zealand.
8.
Johnson, R. A., and Haskell, J. H.(1984). “An approximate lower tolerance bound for the three parameter Weibull applied to lumber property characterisation.”Statistics and Probability, 2(2), 67–75.
9.
Kearney, M. A. (1992). “Fracture strength of notched wood beams,” ME thesis, Dept. of Civ. Engrg., Univ. of Auckland, Auckland, New Zealand.
10.
Lawless, J. F.(1975). “Construction of tolerance bounds for the extreme value and Weibull distributions.”Technometrics, 17(2), 255–261.
11.
Leicester, R. H. (1986). “Confidence in estimates of characteristic values.”Proc., 19th Conf. of CIB-W18, Int. Council for Build. Res. and Documentation, Rotterdam, The Netherlands.
12.
Madsen, H. O., Krenk, S., and Lind, N. C. (1988). Methods of structural safety. Prentice-Hall, Inc., Englewood Cliffs, N.J., 143–144.
13.
Mann, N. R., and Fertig, K. W.(1973). “Tables for obtaining Weibull confidence bounds and tolerance bounds based on best linear invariant estimates of parameters of the extreme value distribution.”Technometrics, 15(1), 87–101.
14.
Mann, N. R., Schafer, R. E., and Singpurwalla, N. D. (1974). Methods for statistical analysis of reliability and life data . John Wiley & Sons, Inc., New York, N.Y.
15.
NAG Fortran library manual; mark 14. (1990). Numerical Algorithms Group, Ltd., Oxford, England.
16.
Natrella, M. G. (1963). “Experimental statistics.”Handbook 91, Nat. Bureau of Standards, U.S. Govt. Printing Ofc., Washington, D.C.
17.
Odeh, R. E., and Owen, D. B. (1980). Tables for normal tolerance limits, sampling plans, and screening. Marcel Dekker Inc., New York, N.Y.
18.
Öfverbeck, P. (1980). “Small sample control and structural safety.”Rep. TVBK-3009, Dept. of Struct. Engrg., Lund Inst. of Technol., Lund, Sweden.
19.
Standard practice for establishing allowable properties for visually-graded dimension lumber from in-grade tests of full-size specimens; D1990-91. (1991). ASTM, Philadelphia, Pa.
20.
Standard practice for evaluating properties of structural lumber; D2915-94. (1994). ASTM, Philadelphia, Pa.
21.
Timber structures standard; NZS 3603:1993. (1993). Standards New Zealand, Wellington, New Zealand.
22.
Walpole, R. E., and Meyers, R. H. (1978). Probability and statistics for engineers and scientists, 2nd Ed., Macmillan Publishing Co., New York, N.Y.
23.
Weibull, W.(1951). “A statistical distribution function of wide applicability.”J. Appl. Mech., 18(3), 293–297.

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Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 122Issue 2February 1996
Pages: 202 - 209

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Published online: Feb 1, 1996
Published in print: Feb 1996

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Authors

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Richard D. Hunt
Timber Engrg. Lect., Dept. of Civ. and Resour. Engrg., Univ. of Auckland, Private Bag 92019, Auckland, New Zealand.
Anthony H. Bryant
Sr. Lect., Dept. of Civ. and Resour. Engrg., Univ. of Auckland, Private Bag 92019, Auckland, New Zealand.

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