PSI - Issue 38

Robin Hauteville et al. / Procedia Structural Integrity 38 (2022) 507–518 Robin Hauteville, Xavier Hermite, Fabien Lefèbvre / Structural Integrity Procedia 00 (2021) 000 – 000

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The Fisher – Snedecor random variable is calculated and assumed to follow a Fisher distribution, allowing estimates of the p-value. The p-value must be compared to the first-order risk, equal to 1 - the confidence level: if the p-value is inferior to the risk, the variances are significantly different.

5.5. Design curve The design curves can be obtained using the equations of probabilistic S-N curve models:

• log( ) = − . log( ) − log . = [ − + ( . )] = − + ( . ) exp [− ( S − + ( . ) ) ] Bastenaire: (22) log and are respectively the residual standard deviation associated with the lifetime and the stress. K is a value defined according to the probability of failure, the one-sided confidence level, the number of tests considered and the number of estimated parameters of the chosen model. To calculate this K-value, two methods are proposed: ISO 12107:2012 method [9]: Called Kc for this method, this factor is given by the standard’s tables up to the probability of survival of (1-p) = 0.999. To calculate this factor for any confidence level, probability level or number of experimental data, an additional algorithm was set up. Indeed, this factor corresponds to the number of standard deviations to be subtracted from a median model to obtain a probability plot considering a level of confidence. The calculation is performed by simulation and iterative process (dichotomy). A batch of random samples of the standard normal variable Z is simulated, with a size equal to the number of test results. For each sample generated, the mean and standard deviation are identified. The dichotomy is performed to find the K factor such that the proportion of (mean - Kc * standard deviation) less than the Z corresponding to the probability level is close to the confidence level. IIW method [13]: This method, recommended especially for welded assemblies, recommends the use of the variable given by the following expression: ( ; 1 − ; ) = −1;1− √ + √ χ − 1 2 −1;1− (23) p: probability of survival allocated to the part, (1 – α): one-sided confidence level, −1;1− : Student's value associated with (n- 1) DDL and having the α probability of exceed ing, : reduced centered normal value with the probability (1-p) of exceeding, χ 2 −1;1− : KHI2 value associated with (n-1) DDL and having the probability (1 – α) of being exceeded. • • (20) (21) • Stromeyer: • Basquin: