Statistical Estimation of the Minimal Resistance Threshold. Case Study of Automotive Heat Exchangers

In the automotive industry, when a component undergoes a request to extend its warranty period (up to 5 or 8 years), the risk assessment needs to consider not only the failures related to non-quality, but also all possible issues originating from wear-out phenomena (durability design failures). The correct identification of a failure-free period affecting wear-out failure mechanisms, such as fatigue or corrosion, is indeed beneficial for reliability of components with a longer warranty period. The durability of the components is experimentally demonstrated by the means of accelerated life tests. Unfortunately, due to the relatively small sample size considered (4 to 8 samples), the location parameter of a three-parameter unimodal distribution (for example Weibull) leads to a failure-free period with an unacceptable level of statistical uncertainty. In this paper, we propose a new methodology for the calculation of the failure-free period defined as a “minimum resistance threshold” (MRT). This threshold is obtained as a weakly scattered deterministic value, from a small population of samples undergoing destructive durability tests. The proposed estimation method is analytically simple and robust. Both physics-of- failure and statistical criteria need to be considered to justify the applicability of the method. The suggested approach makes it possible to obtain an estimator of the location parameter in the case of an ordered sample of small size, without making any a priori hypothesis on the nature of the parent distribution. Several numerical examples will emphasize the advantages of this methodology applied to the risk assessment of design-related warranty failures.