本文裡提出一套利用檢測品質來為鋼橋細部構件選擇最佳的非破壞檢測方法與檢測計劃；各種非破壞性檢測方法對裂縫大小的測得機率函數，可被視為該檢測方法的檢測品質。在考量鋼橋修復之效應後，藉由測得機率、修復之效應與檢測計劃的機率問題，配合蒙地卡羅法對鋼橋中斷裂關鍵構件所模擬的裂縫成長曲線將會有不同之成長過程，因此一條裂縫成長曲線將依照檢測次數（n）的多寡有2n種裂縫成長過程，考量所有蒙地卡羅所模擬之裂縫成長曲線與裂縫成長過程，吾人可以將選擇檢測方法和訂定後續檢測計劃的問題量化成為數學上的最佳化問題，並配合有關結構安全的限制條件，而這個最佳化問題的解，將可為鋼橋「疲勞」或「腐蝕疲勞」檢測問題提供一組最經濟且符合結構安全的檢測方法和檢測計劃。

A probability-based method for selecting an optimal NDI (non-destructive inspection) technique and its associate inspection schedule for fracture-critical members in steel bridges is presented. The probability of detection (POD) function for crack size of an NDI technique is utilized as the measure of inspection quality. Through Monte Carlo simulations for crack growth and repair actions after inspections, n times of inspections could generate 2n kinds of repair scenarios and the corresponding crack growth patterns (curves). Considering all crack growth curves and repair scenarios from Monte Carlo simulations, selecting a suitable NDI technique and its associate inspection schedule for a steel bridge fracture-critical member with the acceptable structural safety requirements becomes a mathematical optimization problem. The solution of the problem can provide an economic and safe inspection strategy for steel bridges against “fatigue” or “corrosion-fatigue” problems.

ASCE Committee on Fatigue and Fracture Reliability, “Fatigue Reliability：Introduction.” Journal of the Structural Division, Proceedings of the American Society of Civil Engineers, ASCD, Vol. 108, No. ST1, pp. 3-23. (1982a).
ASCE Committee on Fatigue and Fracture Reliability, “Fatigue Reliability：Quality Assurance and Maintainability.” Journal of the Structural Division, Proceedings of the American Society of Civil Engineers, ASCD, Vol. 108, No. ST1, pp. 25-46. (1982b).
ASCE Committee on Fatigue and Fracture Reliability, “Fatigue Reliability：Variable Amplitude Loading.” Journal of the Structural Division, Proceedings of the American Society of Civil Engineers, ASCD, Vol. 108, No. ST1, pp. 47-69. (1982c).
ASCE Committee on Fatigue and Fracture Reliability, “Fatigue Reliability：Development of Criteria for Design.” Journal of the Structural Division, Proceedings of the American Society of Civil Engineers, ASCD, Vol. 108, No. ST1, pp. 71-87. (1982d).
Barsom, J. M. and Rolfe, S. T. Fracture and Fatigue Control in Structures: Applications of Fracture Mechanics, 3rd Edition, Butterworth-Heinemann, Massachusetts, USA. (1999).
Berens, A. P. and Hovey, P. W. “Evaluation of NDE Reliability Characterization.” AFWAL-TR-81-4160, Vol. 1, Air Force Wright-Aeronautical Laboratory, Wright-Patterson Air Force Base. (1981).
Berens, A. P. NDE Reliability Analysis. In： Metals Handbook, Vol. 17. 9th ed. ASM International, pp. 689-701. (1989).
Bokalrud, T. and Karlsen, A. “Control of Fatigue Failure in Ship Hulls by Ultrasonic.” Norwegian Maritime Research No.1. (1982).
Cramer, E. H. and Friis-Hansen, P. “Reliability Based Optimization of Multi-Component Welded Structures.” Proceedings of the 11st International Conference on Offshore Mechanics and Arctic Engineering, ASME, Vol. 2, Calgary Canada, pp. 265-271. (1992).
Dowling, N. E. Mechanical Behavior of Materials, Prentice Hall, Englewood Cliffs, New Jersey. (1993).
Engesvik, K. M. and Moan, T.(1983). “Probabilistic Analysis of the Uncertainty in the Fatigue Capacity of Welded Joints.” Engineering Fracture Mechanics, Vol. 18, No.4, pp. 743-762.
Faber, M. H., Sorensen, J. D., Rackwitz, R, Thoft-Christensen, P. and Bryla, P.(1992b).“Reliability Analysis of an Offshore Structure：A Case Study 1.” Proceedings of the 11th International Conference on Offshore Mechanics and Arctic Engineering, ASME, Vol. 2, Calgary Canada, pp. 449-455.
Frangopol, D. M., Lin, K. Y. and Estes, A. “Life-Cycle Cost Design of Deteriorating Structures.” Journal of Structural Engineering, ASCE, Vol. 123, No. 10, pp. 1390-1401. (1997).
Fujita, M., Schall, G. and Rackwitz, R. “Adaptive Reliability-Based Inspection Strategies for Structures Subject to Fatigue.” Proceedings of the 5th International Conference on Structural Safety and Reliability, pp. 1619-1626. (1989).
Hartle, R. A., Amrhein, W. J., Wilson III, K. E., Bauhman, D. R. and Tkacs, J. J. “Bridge Inspector’s Training Manual 90.” FHWA-PD-91-015, Federal Highway Administration, Washington, D. C. (1995).
Harlow, D. G. and Wei, R. P. “Probability Corrosion and Corrosion Fatigue Life,”AIAA Journal, Vol. 32, (10), pp. 2073-2079, (1994).
Laman, J. A. and Nowak, A. S. “Fatigue-Load Models for Girder Bridges.”Journal of Structural Engineering, ASCE, Vol. 122, No. 7, pp. 726-733. (1996).
Kayser, J. R. “The Effects of Corrosion on the Reliability of Steel Girder Bridges,” PhD Thesis, University of Michigan, Ann Arbor, Michigan. (1988).
Kulak, Y. “Prediction of Fatigue Crack Initiation Life Based on Pit Growth,” Corrosion, Vol. 45, (12), pp. 7-11. (1989).
Madsen, H. O., Krenk, S. and Lind, N. C. Methods of Structural Safety, Prentice-Hall Inc., Englewood Cliffs, New Jersey. (1985).
Madsen, H. O., Sorensen, J. D. and Olesen, R. “Optimal Inspection Planning for Fatigue Damage of Offshore Structures.” Proceedings of the 5th International Conference on Structural Safety and Reliability, pp. 2099-2106. (1989).
Manning S. D., Yang, J. N. and Rudd, J. L. “Durability Analysis of Aircraft Structures.” Probabilistic Fracture Mechanics and Reliability, Chapter 5, American Society of Testing and Materials, Special Technical publication. (1986).
Matsuishi, M. and Endo, T. “Fatigue of Metals Subjected to Varying Stress.”paper presented to Japan Society of Mechanical Engineers, Fukuoka, Japan. (1968).
Miner, M. A., Cumulative Damage in Fatigue, J. Appl. Mech., Vol. 12, No. (1945).
Moan, T., Hovde, G. O. and Blanker, A. M. “Reliability-Based Fatigue Design Criteria for Offshore Structures Considering the Effect of Inspection and Repair.” Proceedings of Offshore Technology Conference, pp. 591-600. (1993).
Moses, F., Schilling, C. G. and Raju, K. S. “Fatigue Evaluation Procedures for Steel Bridges.” National Cooperative Highway Research Program Report 299, Transportation Research Board, National Research Council, Washington, D. C. (1987).
Onoufriou, T. “Reliability Based Inspection Planning of Offshore Structures.” Marine Structures, Vol. 12, pp. 521-539. (1999).
Paris, P. C. and Erdogan, F. “A Critical Analysis of Crack Propagation Laws.”Journal of Basic Engineering, ASME, Vol.85, pp. 528-534. (1963).
Rippling, E. R. and Crosley, P. B. Narrative Summary on Fracture Control in Relation to Bridge Design, Federal Highway Administration, Washington, D. C. (1983).
Rudd, J. L. and Gray, T. D. “Quantification of Fastener Hole Quality.” Proceedings of the 18th AIAA/ASME/SAE Structures, Structural Dynamics and Materials Conference. (1977).
Rudd, J. L., Yang, J. N., Manning, S. D. and Garver, W. R. “Durability Design Requirements and Analysis for Metallic Airframe.”Design of Fatigue and Fracture Resistant Structures, ASTM STP 761, pp. 133-151. (1982a).
Rudd, J. L., Yang, J. N., Manning, S. D. and Yee, B. G. W. “Damage Assessment of Mechanically Fastened Joints in the Small Crack Size Range.”Proceedings of the 9th US National Congress of Applied Mechanics. (1982b).
Rudd, J. L., Yang, J. N., Manning, S. D. and Yee, B. G. W. “Probabilistic Fracture Mechanics Analysis Methods for Structural Durability. “Proceedings of AGARD Meeting on Behavior of short Cracks in Airframe Components. (1982c).
Schilling, C. G., Klippstein, K. H., Barsom, J. M., and Blake G. T. “Fatigue of Welded Steel Bridge Members under Variable-Amplitude Loadings.” National Cooperative Highway Research Program Report 188, Transportation Research Board, National Research Council, Washington, D. C. (1978).
Shi, P., Mahadevan, S. “Corrosion Fatigue and Multiple Site Damage Reliability Analysis” International Journal of Fatigue, Vol. 25, pp.457-469. (2003).
Shinozuka, M.(1979). “Durability Methods Development.” Vol. 4: Initial Quality Representation, AFFSL-TR-79-3118. (2003).
Sorensen, J. D., Faber, M. H., Rackwitz, R. and Thoft-Christensen, P. “Modelling in Optimal Inspection and Repair.” Proceedings of the 10th International Conference on Offshore Mechanics and Arctic Engineering, ASME, Vol. 2, Stavanger Norway, pp. 281-288. (1991).
Suwan, S. “Analysis of Structural Plate Mechanical Properties: Statistical Variability and Implications in Structural Reliability.” M. S. Thesis, Department of Civil Engineering, University of Texas at Austin. (2002).
Suwan, S., Manuel, L. and Frank, K. H. ”Statistical Analysis of Structural Plate Mechanical Properties.” PMFSEL R Report No. 03-1, Phil M. Ferguson Structural Engineering Laboratory, The University of Texas at Austin. (2003).
Thoft-Christensen, P. and Sorensen, J. D. “Optimal Strategy for Inspection and Repair of Structural Systems.” Civil Engineering System, Vol. 4, pp. 94-100. (1987).
Yang, J. N. and Trapp, W. J. “Reliability Analysis of Aircraft Structures under Random Loading and Periodic Inspection.” AIAA Journal, Vol. 12, No. 12, pp. 1623-1630. (1974).
Yang, J. N. “Statistical Estimation of Economic Life for Aircraft Structures.” Journal of Aircraft AIAA, Vol. 17, No. 7, pp. 528-535. (1980).
Yang, J. N., Manning, S. D., Rudd, J. L. and His, W. H. “Stochastic Crack Propagation in Fastener Holes.” Journal of Aircraft, AIAA, Val. 22, No. 9, pp. 810-817. (1985).
Yazdani, N. Risk Analysis of Extending Bridge Service Life, PhD Dissertation, University of Maryland. (1984).
Zhao, Z. Primary and Deformation-Induced High and Low cycle Fatigue Reliability of Infrastructure with Updating Through Non-Destructive Inspection, PhD Dissertation, the University of Arizona. (1995).
莊家宏（2006），“檢測品質於鋼橋檢測計劃制定之應用” 國立成功大學土木工程學系，碩士學位論文。
胡永康（2004），“斜張橋設計與施工階段索力分析”，私立中原大學土木工程學系，碩士學位論文。
陳建南（2004），“非破壞檢測方法”，中國非破壞檢驗有限公司。
洪嘉隆（2002），“單索面斜張橋之衝擊系數分析”，國立成功大學土木工程研究所，碩士論文。
鄭文隆（2001），“高屏溪橋”，交通部台灣區國道工程局。
楊國珍（2001），“全銲接斜張橋在活載重下之結構行為”，國立台灣科技大學營建工程系，博士學位論文。
蔡錫鐃（2000），“非破壞檢測試驗”，文京圖書有限公司。