Competing failure with degradation and random shocks based on probabilistic failure threshold

As the products become more and more complicated, and the demands of users vary continuously, failure threshold of product may be probabilistic rather than determined. This paper develops an extension research based on probabilistic failure threshold of competing failure with degradation and random shocks. Firstly, general competing failure model is proposed based on the assumption that the degradation process and the cumulative shock-damage process are independent, and then reliability formula based on different distribution is elaborated. Secondly, another competing failure model based on probabilistic failure threshold is proposed with the consideration of dependent competing of degradation and random shocks based on the former model. Random shocks could affect degradation process with a damage factor, which adds to the probability of degradation failure to the product. At last, those two models are applied to two cases of accelerator with degradation data and vibrating-damage data, and the comparison reveals the differences between those two models as well as the traditional model with pre-determined threshold. It tests the reasonability and accuracy of the probabilistic threshold competing failure models. The result of this paper provides an extensional method for the product failure prediction and healthy management based on the competing failure modes of probabilistic threshold degradation and random shocks.