Planning fatigue experiments and analyzing fatigue data with the random fatigue-limit model and modified sudden death tests

In this research, we address important issues faced by researchers in fatigue testing. We suggest a practical model to describe the relationship between fatigue life and applied stress, illustrate the corresponding data analysis methods, and study test plans under this model. We also present test plans that provide a systematic and efficient use of a limited number of test positions. These methods emphasize the importance of accuracy in the study of fatigue life while recognizing physical realities and resource limitations.;In a fatigue-limit model, test units tested below the fatigue limit (also known as the threshold stress) theoretically will never fail. We use the random fatigue-limit model to describe: (a) the dependence of fatigue life on the stress level, (b) the variation in fatigue life, and (c) the unit-to-unit variation in the fatigue limit. We fit the model to actual fatigue data sets by maximum likelihood methods and study the fits under different distributional assumptions.;Using the random fatigue-limit model, we present methods for planning future life tests. We obtain planning values from an actual fatigue experiment and use these to plan future tests. Based on an optimization criterion, we compute best traditional (equally-spaced stress levels with equal allocations of test units) and general (arbitrary choices for stress levels and allocations) plans with 3 and 4 stress levels. The results here serve as guidelines for planning actual tests.;We present modified sudden death test (MSDT) plans to address the problem of limited testing positions in single population life tests. A single MSDT involves testing k specimens simultaneously until the rth failure. The complete MSDT plan consists of g single MSDTs run in sequence. We evaluate test plans with respect to the asymptotic variance of maximum likelihood estimators of quantities of interest, total length of the experiment and sample size.