Determination of the Three-Parameter Weibull Distribution and Confidence Bands From Experimental Fatigue Strength Data

The S-N curve for the material used to make a pressure vessel is approximate because it is drawn from a limited number of test specimens. The resulting curve may be in error due to a variety of factors including surface condition, size, environment conditions, and stress concentrations. As a result, when the fatigue strength like the endurance limit is determined from the S-N curve by observing a definite break in the curve, it will be subject to error. Because of these uncertainties, it is necessary to use appropriate statistical methods to interpret the test results. In this paper, it is assumed that the percentage of failures for a given service life can be approximated by a three-parameter Weibull distribution. The Weibull distribution is flexible and has been shown to be suitable for structural reliability. The distribution is fitted to experimental data using a least square best fit approach applied to a discrete version of the cumulative probability distribution function, F(x). In practice a point-by-point estimate of the cumulative distribution function is used. As a result, it is necessary to establish confidence bands. The true curve of F(x) lies within these bands for a given probability.