一階可靠度方法(First-order reliability method；FORM)是利用設計點( Design point )上的線性方程式來近似統御方程式( Performance function)，所以當統御方程式為極度非線性時，就不適合使用FORM來做可靠度分析。為了改善FORM 不適用在統御方程式為極度非線性上的缺點，二階非線性可靠度方法(Second-order reliability method；SORM )被提出，但是在利用SORM進行可靠度分析時，在計算Hessian矩陣的特徵值時，會因處理龐大的隨機變數而使得求取統御方程式的梯度變得相當繁雜，使得SORM變得難以應用在實際工程上。本文利用經驗二階可靠度指標來改善之前SORM中轉換以及梯度等方面的問題，使得在可靠度分析上能夠很容易地應用SORM而不失準確度。
本文以26萬頓油輪為例，考慮油輪在不同海況下，利用FORM與SORM求取船體結構的破壞機率，並比較之，其中SORM是以點逼近統御方程式(Point-fitted Performance function)的概念進行之。

【1】 Breitung, K., “Asymptotic approximation for multi-normal integer,” J. Engrg. Mech., ASCE, 110(3), 357-366,1984
【2】 Caldewll, J. B., “Ulitimate Longitudinal Strength,” Transactions, Royal Institution of Naval Architects, Vol. 107, 1965.
【3】 Chao, R. J., and Ayyub, B. M., “Reliability and Uncertainty Evalution for Longitudinal Bending of Hull Girders of Surface Ships,” Journal of Ship Research, Vol. 41, No. 1, pp. 57-68, March, 1997.
【4】 Der Kiureghian, A., Lin, H. Z., and Hwang, S. J., “Second-order reliability approximations,” J. Engrg. Mech., ASCE, 113(8), 1208-1225, 1987
【5】 Der Kiureghian, A., and De Stefano, M., “Efficient algorithm for second-order reliability analysis,” J. Engrg. Mech., ASCE,117(12), 2904-2923, 1991
【6】 Fiessler. B., Neumann, H. –J, and Rackwitz, R., “quadratic limit state in structural reliability,” J. Engrg. Mech., ASCE, 105(4), 661-676, 1979
【7】 Hasofer, A. M., and Lind, N. C., “Exact and Invariant Second-moment Code Format,” Journal of Engineering Mechanics, ASCE, Vol. 100, No. EMI, pp. 111-121, Feb., 1974.
【8】 Hohenbichler, M., and Rackwitz, R., “Improvement of second-order reliability estimates by importance sampling,” J. Engrg. Mech., ASCE, 114(12), 2195-2199,1988
【9】 Loukakis, T. A., and Chryssostomos Chryssostomidis, “Seakeeping Standard Series for Cruiser-stern ships,” Trans. SNAME, Vol. 83, pp67-127, 1975.
【10】 Mansour, A. E., “Methods of Computing the Probability of Failure Under Extreme Values of Bending Moment,” J. Ship Research, Vol. 16, No. 2, pp. 113-123, June, 1972.
【11】 Mansour, A. E., “An Introduction to Structural Reliability Theory,” Ship Structure Committee Report, SSC-351,Dec., 1986.
【12】 Mansour, A. E., “Extreme Value Distributions of Wave Loads and Their Application to Marine Structures,” Proceedings, Marine Structural Reliability Symposium, Arlington, Va., Oct., 1987.
【13】 Mansour, A. E., Yang, J. M. and Thayamballi, A., “An Experimental Investigation of Ship Hull Ultimate Strength,” Transactions SNAME, pp. 411-439, 1990.
【14】 Mansour, A. E., and Hovem L., “Probability Based Ship Structural Safety Analysis,” Journal of Ship Research, Vol. 38, No. 4, pp. 329-339, Dec., 1994.

【15】Nitta, A., Arai, H. and Magaino, A., “Basic of IACS unified longitudinal strength standard,” Marine structures, Vol. 5, pp. 1-21,1992
【16】 Murray N. W., “Introduction to the Theory of Thin-Walled Structures,” Oxford Engineering Science Series 13, Clarendon Press, Oxford, pp. 54-135, 1986.
【17】 Paik, J. K., and Lee, J.M., “An empirical formulation for predicting the ultimate compressive strength of plates and stiffened plates” Proceedings of the Seventh International Offshore and Polar Engineering Conference, pp. 328-338, 1997
【18】 Paik, J. K., Thayamballi, A. K. and Che, J. S., “Ultimate Strength of Hulls Under Combined Vertical Bending, Horizontal Bending, and Searing Forces,” Transactions SNAME, Vol. 104, pp. 31-59, 1996.
【19】 Paik, J. K., Kim, S. K., Yang, S. H. and Thayamballi, A. K., ”Ultimate Strength Reliability of Corroded Ship Hulls,” The Royal Institution of Naval Architects, pp. 1-18, 1997.
【20】 Paik, J. K., Thayamballi, A. K., and Yang S. H., ” Residual Strength Assessment of Ship After Collision and Grounding,” Maine Technology,Vol.35,No.1, pp 38-54, Jan.1998.
【21】 Rackwitz, R. and Fiessler, B., “Structural Reliability under Combined Random Load Sequence,” Computers and Structures, Vol. 9, 1978.
【22】 Rahman, M. K., “Applied Probability and Stochastic Process,” In Engineering and Physical Sciences, University of Florida.
【23】 Timoshenko, S. P. and James M. G., ”Theory of Elastic Stability,” McGraw-Hill Press, Second Edition.
【24】 Loukakis, T. A., and Chryssostomos Chryssostomidis, “Seakeeping Standard Series for Cruiser-stern ships,” Trans. SNAME, Vol. 83, pp67-127, 1975.
【25】 Tvedt, L., “Two second-order approximations to the failure probability,” Veritias Rep. RDIV/20-004083, Det norske Veritas, Oslo, 1983
【26】 Tvedt, L., “Second-order reliability by an exact integral,” Proc., 2nd IFIP Working Conf. on reliability and Optimization on Struct. Sys., P. Thoft-Christensen, ed., Springer, New York, 377-384,1988
【27】 Tvedt, L., “Distribution of quadratic forms in normal space application to structural reliability,” J. Engrg. Mech., ASCE, 116(6), 1183-1197, 1990
【28】 Vesta, J., “Lessons Learned from Full-Scale Ship Structural Tests,” SNAME Annual Meeting, pp. 1-39, New York, 1959.
【29】 Zhao, T. G., and Ono, T., “New approximation for SORM: Part 1, ”. Engrg. Mech., ASCE, 125(1),79-85,1999

【30】Zhao, T. G., and Ono, T., “New approximation for SORM: Part 2, ”. Engrg. Mech., ASCE, 125(1),86-93,1999
【31】 洪振發, 李昱君, “多破壞模式之結構系統可靠度,” 國立台灣大學造船及海洋工程學研究所, NTU-NAOE-Tech.Report 464, June, 1994
【32】 陳俊達, “船舶結構受創後之剩餘強度與可靠度分析, ” 國立成功大學造船及船舶機械工程研究所, 碩士論文, 中華民國89年6月