Wet multi-disc clutch is a critical component within the vehicle’s integrated transmission system，where the accurate online prediction of remaining useful life (RUL) plays a key role in ensuring the operational safety and formulating the condition-based maintenance strategies.A bivariate degradation model with common random variable based on inverse Gaussian processes is developed.The correlation between variables is characterized by a common random variable.The Bayesian method is used for the posterior estimation of model parameters，and the index for goodness-of-fit test is proposed.Considering the operation and maintenance process of wet clutch equipment，the solving method for its dynamic failure rate and availability is derived，and an online RUL prediction method based on Monte Carlo simulation is proposed.The effectiveness of the proposed model is verified with different sample sizes through simulation study and degradation analysis of wet clutch tests.Compared to traditional Gamma models，the proposed bivariate inverse Gaussian process model is enable to accurately estimate the failure rates and availability of wet clutch and complete more precise online RUL prediction.