Design Curve Construction Based on Tolerance Limit Concept

Abstract

The design curves, such as fatigue design S-N curves, required in engineering designs, are usually constructed by analyzing test data, which often exhibit large scatter. There are many methods available to construct a design curve and many of these methods, with varying degrees of conservativeness, accuracy, and simplicity, have been adopted by engineering standards, codes and guidelines, such as the ASME and ASTM codes and standards. However, to meet the increasing engineering demands, a simplified, user friendly engineering method with rigorous mathematical and physical basis is still urgently needed to accurately manage the margin of safety on one hand and decrease the cost on the other hand. In this paper the current engineering practices for constructing a design curve is reviewed. It is followed by the tolerance limit concept for general regression cases, because of its capability to relate the design curve to sample size, probability, and confidence level. A simple approximate solution is derived for Owen’s tolerance limit approach, which previously could be solved only with a very complex procedure. Finally, recognizing the physical unsoundness of the hyperbolic shape of the design curves constructed with the Owen’s tolerance limit approach, a new simple design curve construction method is proposed based on the “equal partition principle”. The predicted results from the new method are compared with that of other methods and the advantage of the proposed procedure over other methods is demonstrated with several worked examples. Linear design curve construction with heteroscedastic characteristics (variable variance) and nonlinear design curve are also discussed.