A typical SN curve identifies the 50% fracture rate for a given level of loading.  But if we can’t possibly accept that 50% of our devices will fracture when we are designing medical implants.

So we need to do some statistical analysis of the data coming from a fatigue test and determine what the limit load would be, at say a 5% fracture rate.  Such analysis is readily available when you employ an optimal sampling technique to determine the load levels during a fatigue experiment.  Even if you don’t employ an optimal sampling technique, you can still determine fracture rates for other than 50%.  But the resulting confidence will depend on how well you chose the sample levels to be tested.

The plot on the left demonstrates how effective an optimal sampling technique can be.  Red circles indicate samples that survived 1M cycles and green crosses denote samples that fractured.  After about the 10th specimen the algorithm settles into a narrow band converging on an estimate of the 50% fracture level and the associated standard deviation.  Another way to look at the data is the plot on the left below, which shows the relationship between the estimate and standard deviation for a specified confidence.  A likelihood ratio analysis plot for this data is shown in the figure on the right below for a confidence of 95%.  From this plot we would expect a 1% fracture rate for a loading of +/-0.8%.