Linear Model in Probabilistic Fatigue Design

by Paul H. Wirsching, (A.M.ASCE), Assoc. Prof.; Aerospace and Mech. Engr., Univ. of Arizona, Tucson, Ariz.,
Steve Hsieh, Grad. Asst.; Aerospace and Mech. Engr., Univ. of Tucson, Tucson, Ariz.,

Serial Information: Journal of the Engineering Mechanics Division, 1980, Vol. 106, Issue 6, Pg. 1265-1278

Document Type: Journal Paper


The conventional method of linear model analysis is used to analyze data on correlated variables (Y and X). But the methods used to define a design curve seldom account for statistical uncertainty in the estimates of the parameters a and b in the linear relationship, Y=a + bX. The independent variable is X. Unconservative design result. Using S-N fatigue data analysis as an example, a method of establishing a design curve, based on predicition intervals, was derived. This method was also used to provide the necessary statistical information for probabilistic design format. To account for the statistical uncertainty in estimates of a and b, the simple standard deviation of Y given X is expanded.

Subject Headings: Linear analysis | Probability | Fatigue (material) | Parameters (statistics) | Curvature | Uncertainty principles

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