Optimal S/N Fatigue Testing for Stochastic Service Loads

An optimal protocol for stress range/number of cycles $(S∕N)$ life testing is developed. The objective is to obtain an $S∕N$ curve that will minimize the error in predictions of the service life, taking into account the fact that there is always uncertainty about an $S∕N$ curve derived from limited testing. The mathematical results apply to any problem in which there is uncertainty not only about the properties of the specimen, but also about the stress ranges that will be applied under service loads. It is shown that finding the testing procedure that will truly minimize the mean-squared error requires the solution of a quartic equation, but good approximate results can be obtained from the roots of a quadratic equation. Furthermore, it is easy to determine the consequences of using a nonoptimal testing procedure. The results are illustrated by their application to simple and commonly used models for fatigue prediction. Some numerical integration is required when the method is applied for most distributions of service stress ranges, but this is not true for the log-normal distribution and graphical results are presented which allow direct application for the popular Weibull model.