Backwards statistical inference method for P–S–N curve fitting with small-sample experiment data

• The innovative idea and efficient method to quantify the failure trajectory concept.
• Backwards statistical inference technique to fit P–S–N curve by small sample data.
• The strategy to search the life standard deviation – stress relationship.
• The method saves specimens, shortens test time and keeps a quite high accuracy.
• Simple and mathematically traceable, involving no impractical assumption.

Based on the failure trajectory concept and backwards statistical inference technique, experimental programs are designed to fit P–S–N curve with a small number of test data. Underlying the program is a method to convert fatigue lives tested at different cyclic stress levels into the equivalent lives at an arbitrary stress level, by which a relatively large size sample is established. The basic justification is that the probability distribution of the equivalent lives is identical to that of the real life distribution at the same stress level, only if the conversion is based on the correct life distribution – stress relationship. Consequently, parameters characterizing P–S–N equation can be acquired through a process to search reasonable life distribution – stress level relationship, by means of statistically testing the difference between equivalent life distribution and the real life distribution, that is either obtained by a large size sample of fatigue life test data or reasonably provided.