Reliability modelling with uncertain threshold and fractional differential degenerate equation in uncertain environment

Abstract

A dependent competitive failure model of Caputo uncertain fractional differential equation (UFDE) degradation with uncertain threshold is proposed. There are two main reasons for the failure of an equipment or system, long-term natural wear and the impact of external loads. Each shock will cause a sharp increase in wear. In the absence of fault data, the natural wear process is driven by a Caputo type of UFDE, and the external load is an uncertain renewal reward process. Three different shock models are considered and calculated the belief reliability of device according to uncertainty theory, taking the jet pipe servo control valve as an example, the proposed model is simulated, and the results show that the proposed model is effective.