PSI - Issue 19

Xavier Hermite et al. / Procedia Structural Integrity 19 (2019) 130–139 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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law, also called Basquin’s model, combined with the Palmgren – Miner’s rule [5, 6] ). The first and most frequently used approach is to compute a simple test specification based on a sinusoidal load cycle repeated as-is (or as block of different ranges) by the theory of fatigue damage equivalency. Another approach is to focus on the most damaging life situations and reproduce them on the test bench. The bench is then generally more complex, but the load cycles are much more representative of the real life. Next to these first considerations comes the expectations around the test: the reliability target to demonstrate, and the insurance of a representative test relative to in-service life. This last point excludes immediately the well-known censored tests, which cannot reveal the failure mechanism nor its associated failure mode. Yet, censored tests are often the best way to reduce test duration. Thus, different cases must be considered. For well-known systems, a reliability demonstration can be needed when usage changes (in load, for instance to propose the system to a new public, and/or in duration, for instance to extend a warranty period). Censored testing is in this case the best way to reduce test duration, because the failure mechanisms and their associated failure modes are usually known, and the test bench has already been designed, used and approved. The test specification is then built through the Weibayes method: = (− ∙ 12 − (2) 2 ∙ ∙ ( ) ) 1 ⁄ - t is the test duration, during which no failure should occur, - T target is the targeted lifetime for reliability demonstration, -  is the Weibull form parameter, generally taken between 1.5 and 3 for fatigue mechanism, - 1-  is the confidence level associated to the reliability demonstration, -  ² 1-  (2) is the chi-squared random variable associated to 2 degrees of freedom and a probability 1-  to be exceeded, - N is the number of test sample(s), - R target is the reliability target to demonstrate. It is very important to point out that for wear-out mechanism such as fatigue, the test duration must be representative: testing 10 000 systems for 10 load cycles doesn’t make sense, even if it mathematically demonstrates a reliability target! For a system similar to another, whose reliability is known or demonstrated by experience, the approach depends on the similarity. For a new manufacturing process (for instance for a supplier sourcing) under the same design and in-service conditions, a strength comparison test might be the best strategy to reliability demonstration: at least 3 samples of each systems under the same load case until fatigue breakage and statistical comparison of the test lifetime to assess the benefit of the new feature. For any other case, the experience feedback of the similarity can be exploited through a Bayesian approach to define the best test specification: a priori + likelihood → a posteriori - a priori is defined by the experience feedback on the similar condition, - the likelihood is the test result on the system, - a posteriori is defined by the reliability target. Reversing the Bayesian approach to assess the statistical property to demonstrate by testing from the reliability target and the experience feedback of a similar system may involve computational means, but the likelihood is usually less restrictive in terms of test duration. However, care is inherent to the Bayesian method: systems must be similar (design, process, mission profile, etc.) and experience feedback must be representative (completeness, correct analysis method, unbiased data, etc.). For any other case, the test specification should be built from a warranty factor and a test factor applied to the mission profile in order to accelerate the test duration (see Figure 5). The warranty factor depends on the reliability target and the statistical distribution of the mission and strength profiles (distribution law and coefficient of variation). Mission profile statistical distribution should be assessed by