Integrated Evaluation of Constant Amplitude Life Tests Towards SN Curves and Endurance Limit

Establishing SN curves from constant amplitude life tests and locating the endurance limit are indispensable tasks in durability engineering. For both regimes, finite life and endurance limit, there are many approaches available, like linear regression or maximum likelihood. Especially on low load levels, tests may run very long and one may suspend them before failure. Especially the staircase method for evaluating the endurance limit systematically produces almost 50 percent suspended results. Hence, when data for both regimes is available, those run-outs need to be considered in a statistically proper way. If both regimes are evaluated separately it is often ambiguous if a single observation may be used for estimating the endurance limit or for the finite life regime.
In this paper, we present an integrated approach, for simultaneous evaluation of both regimes. Every single observation is mapped to one of the regimes with certain probabilities. Even more general, our model suggests the optimal model complexity for the data: Single SN curve, only endurance limit, SN curve with two slopes or SN curve with inflection point towards endurance limit. To achieve this, we combine the well-known maximum likelihood principle with Akaike’s information criterion to find the best model.
Although most ingredients are known in SN curve estimation, the authors believe that the integrated approach is neither widely known nor routinely applied. We explain the approach in detail on a real-life example to discuss drawbacks and advantages, especially the beneficial support for the engineer to find the optimal model complexity.