Optimal test planning for the fatigue-limit model when the fatigue-limit distribution is known

This article discusses tools for planning life tests under the random fatigue-limit model, when the form of the fatigue-limit distribution is completely specified. Expressions for the Fisher information matrix elements are provided. Test-plan objectives, such as minimum variance of quantile or parameter estimator, can be written in terms of these expressions. Under Type I censoring, all experimental conditions can be described by a standardized slope parameter & a standardized log(censoring time). This article provides equivalence theorems, which can be used to check the optimality of test plans which often have two levels. The best three-level standard test plans are not optimal, but, in general, involve fewer extrapolations to low stresses than the optimal plans. Test plans for a titanium-alloy fatigue test are presented to illustrate the methods.