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What is Learnable in Valiant's Theory of the Learnable? 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Reliability Analysis of Systems Subject To Mutually Dependent Competing Failure Processes With Changing Degradation Rate
Nooshin Yousefi, David W. Coit · 2019-03-01 · via math.ST updates on arXiv.org

In this paper, a new reliability model has been developed for a single system degrading stochastically which experiences soft and hard failure. Soft failure occurs when the physical deterioration level of the system is greater than a predefined failure threshold, and hard failure occurs when the instantaneous stress caused by a shock process is greater than a critical threshold. It is considered that the degradation and shock process are mutually dependent. In fact, each arriving shock accelerates the degradation process by adding abrupt additional damages to the degradation path and changing the degradation rate according to specific magnitude; also, the cumulative degradation changes the occurrence intensity of shock process. A gamma process is used as a stochastic process to model the degradation path. A realistic numerical example is presented to illustrate the proposed reliability.

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